Entrance Exam – Page 7

JEE Main Physics Kinematics Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Kinematics Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Kinematics Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction. [1983-1 mark]
a) due north b) 30° east of north
c) 30° west of north d) 60° east of north
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2.A boat which has a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minute. The velocity of the river in the shortest time. The velocity of river water in km/hr is [1988-1 mark]

Ans.

3.A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with speed v. Friction between the bead and the string may be neglected. Let t_p and t_Qbe the respective times taken by P and Q to reach the point B. Then[1993-2 marks]

Ans.(a)Horizontal displacements of both, the particle and bead, p and Q are equal Bead Q moves along AB with a constant velocity v. For particle P, motion between AC will be under acceleration while between CB will be under retardation. The horizontal component of its velocity may be greater than or equal to v. It will not be less than v.Obviously, t_P < tQ.

4.In 1.0 sec. a particle goes from point A to point B, moving in a semicircle of radius 1.0 m as shown in the figure. The magnitude of the average velocity is :

a) 3.14 m/sec b) 2.0 m/sec
c) 1.0 m/sec d) zero
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5.A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as

Ans.

(ii)Initial velocity is downwards and therefore negative. After collision, it reverses its original direction with smaller magnitude. The velocity is upwards. Graph (a) satisfies these conditions.

6.A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be [2004]

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7.A small block slides, without friction, down an inclined plane starting from rest. Let S_n be the distance travelled from time t = (n – 1) to t = (n.) Then S_{n/S_n+1} is [2004-2 marks]

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8.The veiocity dispKiicement graph of a particle moving along a straight line is shown. The most suitable acceleration-displacement graph will be

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9.A ball A ball of mass 0.2 kg rests on a vertical of heights 5 m. A bullet of mass 0.01 kg, travelling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. They hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is [2011]

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Multiple Choice with ONE or More Than ONE correct answers
10.A particle is moving eastwards with a velocity of 5m/s. In 10s the velocity changes to 5m/s northwards. The average acceleration in this time is [1982-3 marks]

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12.The co-ordinates of a particle moving in a plane are given by x (t) = a cos (pt) and y (t) = b sin (pt) where a, b (< a) & p are positive constants of appropriate dimensions. Then [1999-3 marks]

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13.A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of V J contact, B is the centre of a the sphere and C is topmost point, Then,[2009]

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14.Column-I describes some situations in which a small object moves. Colymn-H describes some characteristics of these motions. Match the situations in column-I with the characteristics in column-II. [2007-6 marks]

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15.Column-I gives a list of possible set of parameters measured in some experiments.The variations of the parameters in the form of graphs are shown in Column-II. Match the set of parameters given in Column-I with the graphs given in Column-II.

Assertion & Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-l and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase
d)Statement-1 is false, statement-2 is true.

16.Statement -1 : For an observer looking out through the window of a fast moving train the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

Ans.

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18.Is the time variation of position shown in the figure observed in nature ? [1979]

Ans.If we draw a straight line parallel to x-axis, it cuts the given figure at 2 points indicating that at one time, the,particle is at two different positions which is absurd. Thus such a motion as shown in the figures is never observed in nature.

19.Particles P and Q of mass 20 g and 40g respectively are simultaneously projected from points A and B on the ground.The initial velocities of P and Q make 45° and 135° angles respectively with the horizontal AB as shown in the figure. Each particle has an initial speed of 49m/s. The separation AB is 245m. Both particle travel in the same vertical plane and undergo a collision. After the collision, P retraces its path. Determine the position of Q when it hits the ground. How much time after the collision does the particle Q take to reach the ground ? Take g = 9.8m / s² [1982-8 marks]

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20.A body falling freely from a given height H hits an inclined plane in its path at a height h. As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of (h/H) the body will take maximum time to reach the ground?
Ans.PQR is an inclined plane. The body falls under gravity vertically from A to B till it strikes the inclined plane. At B, its velocity is horizontal. From B to C, the body follows a parabolic path. At C, it reaches the ground.

21.Two towers AB and CD are situated a distance d apart as shown in figure. AB is 20 m high and CD is 30m high from the ground. An object of mass m is thrown from the top of AB horizontally with a velocity of lOm/s towards CD. Simultaneously another object of mass 2m is thrown from the top of CD at an angle of 60°^t0the horizontal towards AB with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane, collide in mid-air and stick to each other [1994-4 marks]

i)Calculate the distance d between the towers and,
ii)Find the position where the objects hit the ground.
Ans.

Ans.

23.A cart is moving along x-direction with a velocity of 4m/s. A person on the cart, throws a stone with a velocity of 6m/s, relative to himself. In the frame of reference of the cart, the stone is thrown in y-z plane making an angle of 30° with vertical z-axis. At the highest point of its trajectory, the stone hits an object of equal mass, hung vertically from branch of a tree, by means of a string of length L. A completely inelastic collision occurs in which the stone gets embedded in the object. Determine:[1997-5 marks]
i) the speed of the combined mass immediately after the collision with respect to an observer on the ground
ii)the length L of the string such that tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.
Ans.i) The cart is moving in x-y plane
The stone, thrown from cart, travels in y-z plane while z-axis is vertical axis. The stone makes an angle of 30° with z-axis. Its path is parabolic. At the highest point of its trajectory, the vertical velocity of the stone will be zero. The velocity of the stone is thus confined to (x, y) plane at the highest point. Velocity of cart is along x-axis

ii)It is given that the tension in the string becomes zero at horizontal position. The combined mass therefore is at rest in this position. During the subsequent motion of the combined mass, the energy is conserved.

Ans.

26.A particle is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance L/8 from O as shown in figure. The object is given a horizontal velocity u. At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Find u. [1999-10 marks]

Ans.OP denotes string of length L. The particle starts from P with a horizontal velocity u. It travels along a circular path till Q. Then it passes the line AB. At Q, motion ceases to be circular. At C, its velocity is horizontal, where the particle crosses AB. After Q, the particle performs a projectile motion. At C, the velocity becomes horizontal. Thus C is at the highest point of projectile motion

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29.

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True / False Type
30.Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed (Neglect air resistance).[1983-2 marks]
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31.’A projectile fired from the ground follows a parabolic path. The speed of the projectile, is minimum at the top of its path. [1984-2 marks]
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32.Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails [1985-2 marks]
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Fill in the blanks
33.A particle moves in a circle of radius R. In half the period of revolution its displacement is………. and distance covered is……… ……….. [1983-2 marks]
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34.Four persons K,L,M,N are initially at the four corners of a square of side d. Each person now moves with a uniform speed vin such a way that K always moves directly towards L, L directly towards M,M directly towards N, and N directly towards K. The four persons will meet at a time ………….. [1984-2 marks]
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36.The trajectory of a projectile in a vertical plane is y = ax-bx²,where a, b are constants, and x and y are respectively the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained is……….and the angle of projection from the horizontal is [1997-2 marks]
Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Physics Waves Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Waves Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Waves Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.A wave represented by the equation y = acos(kx — wt) is superposed with another wave to form a stationary wave such that point x=0 is a node. The equation for the other wave is [1988-1 mark]

2. An object of specific gravity p is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is 300 Hz. The object is immersed in water so that one half of its volume is submerged. The new fundamental frequency in Hz is [1995-2 marks]

3.The extension in a string, obeying Hooke’s law, is x . The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5 x , the speed of sound will be [1996-2 marks]
a) 1.22 v b) 0.61 v c) 1.50 v d) 0.75 v

4.An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe . The fundamental frequency of the open pipe is :[1996-2 marks]
a) 200 Hz b) 300 Hz
c) 240 Hz d) 480 Hz

5.A whistle giving out 450 Hz approaches a stationary observer at a speed of 33 m/s. The frequency heard by the observer in Hz is : (speed of sound = 330 m/s) [1997-1 mark]
a) 409 b) 429 c) 517 d) 500

6.A travelling wave in a stretched string is described by the equation y = A sin (kx – wt) . The maximum particle velocity is : [1997-1 mark]
a) Aw b) w/k c) dw/dk d) x/t

7.A train moves towards a stationary observer with speed 34m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the train’s speed is reduced to 17m/s, the frequency registered is f₂. If the speed of sound is 340m/s then the ratio f1/f₂ is[2000-2 marks]
a) 18/19 b) 1/2 c) 2 d) 19/18

8.Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental nodes, the one of length L with frequency f1 and the other with frequency f₂. The ratio f1/f₂ is given by [2000-2 marks]
a) 2 b) 4 c) 8 d) 1

9.Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds, the total energy of the pulses will be [2001-2 marks]

a) zero
b)purely kinetic
c)purely potential
d)partly kinetic and partly potential

10.The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is y_t = A sin(px/L) sin wt and energy is Ej and in another experiment its displacement is y₂=Asin(2px/L) sin 2wt and energy is E₂. Then [2001-1 marks]
a) E₂ = E1 b) E₂ = 2E1
c) E₂= 4E1 d) E₂ = 16E1

11.A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is [2002-2 marks]
a) 242/252 b) 2 c)5/6 d) 11/6

12.A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is [2002-2 marks]
a) 25 kg b) 5 kg c) 12.5 kg d) 1/25 kg

13.A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beat. [2003-2 marks]

a) 33 m/s b) 22 m/s c) zero d) 11 m/s

14.In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1m. When this length is changed to 0.35m, the same tuning fork resonates with the first overtone. Calculate the end correction. [2003-2 marks]
a) 0.012 m b) 0.025 m
c) 0.05 m d) 0.024m

15.A pipe of length l1 closed at one end is kept in a chamber of gas of density p1 . A second pipe open at both ends is placed in a second chamber of gas of density p₂. The compressibility of both the gases is equal. Calculate the length of the second pipe if frequency of first overtone in both the cases is equal [2004-2 marks]

16.A source of sound of frequency 600 Hz is placed inside water. The’speed of sound in water is 1500m/s and in air it is 300m/s. The frequency of sound recorded by an observer who is standing in air, is [2004-2 marks]
a) 200 Hz b) 3000 Hz c) 120 Hz d) 600 Hz

17.In a resonance tube with tuning fork of frequency 512 Hz, first resonance occurs at water level equal to 30.3cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is [2005-2 marks]
a) 51.2cm/s b) 102.4cm/s
c) 204.8cm/ s d) 153.6cm/s

18.An open pipe is in resonance in 2^nd harmonic with frequency f1. Now one end of the tube is closed and frequency is increased to f₂ such that the resonance again occurs in _nth harmonic. Choose the correct option [2005-2 marks]

19.A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to ‘x’. Further, it is observed that the frequency of 1^st harmonic (fundamental frequency) in AB is equal to 2^nd harmonic frequency in CD. Then, [2006-3 marks]

20.In the experiment to determine the speed of sound , using a resonance column, [2007-3 marks]
a)prongs of the tuning fork are kept in a vertical plane
b)prongs of the tuning fork are kept in a horizontal plane
c)in one of the two resonaces observed, the length of the resonating air column is close to the wavelength of sound in air.
d)in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air.

21.A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snapshot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is.[2008]

22.A vibrating string of certain length / under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n.Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340m/s, the frequency n of the tuning fork in Hz is [2008]
a) 344 b) 336 c) 117.3 d) 109.3

23.A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms¹, the mass of the string is
a) 5 grams b) 10 grams c) 20 grams d) 40 grams

24.A police car with a siren of frequency 8kHz is moving with uniform velocity 36km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is (2011)
a) 8.50 kHz b) 8.25 kHz
c) 7.75 kHz d) 7.50 kHz

Multiple Choice with ONE or More Than ONE correct answers
25.A wave equation which gives the displacement along the y-direction is given by y = 10^-4 sin (60t + 2x) where x and y are in metre and t is time in second. This represents a wave

27.An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (V=330ms^_1) [1985-2 marks]
a) 31.25 b) 62.50
c) 93.75 d) 125

28.A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512 Hz. If the tube is open at both ends the fundamental frequency that can be excited is (in Hz) [1986-2 marks]
a) 1024 b) 512 c)256 d) 128

29.The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are [1987-2 marks]

30.An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P₂ open at ends vibratting in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P₂ is [1988-2 marks]
a) 8/3 b)3/8 c)l/6 d) 1/3

JEE Main Home Maths Physics Chemistry

JEE Main Mathematics Quadratic Equations And Expressions Previous Year Papers Questions With Solutions

December 14, 2022

JEE Main Mathematics Quadratic Equations And Expressions Previous Year Papers Questions With Solutions

Ans.

Ans.(1) p + q = -p and pq = q => q(p-1)=0 => q=0 or p=1.
If q = 0, then p = 0. i.e., p – q\p = 1 and q = -2.

Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Physics Work, Energy And Power Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Work, Energy And Power Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Work, Energy And Power Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.Two masses of 1 g and 4g are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is [1980-2 marks]

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2.If a machine is lubricated with oil [1980-2 marks]
a)the mechanical advantage of the machine increases
b)the mechanical efficiency of the machine increases
c)both its mechanical advantage and efficiency increase
d)its effeciency increases, but its mechanical advantage decreases.
Ans.(b) When a machine is lubricated with oil friction decreases. Hence the mechanical efficiency of the machine increases.

3.A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a_c is varying with time ‘t’ as a_c = k²rt²where ‘k’ is a constant. The power delivered to the particle by the force acting on it is[1994-1 mark]

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4.A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest positon, and has a speed u. The magnitude of the change in its velocity as it reaches a positon where the string is horizontal is [1998-2 marks]

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5.A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of[1999-2 marks]
a) (2/3) k b) (3/2) k c) 3k d) 6k
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6.A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to [2000]
a) v b) v² c) v³ d) v⁴
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7.A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F (x) = -kx + ax³. Here k and a are positive constants. For x>0, the functional graphically form of the potential energy U(x)of the particle is [2000]

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8.An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is [2002]

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9.If W1, W₂ and W₃ respresent the work done in moving a particle from A to B along three different , paths 1,2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W₂ and W₃[2003]

a)W1>W₂>W₃
b)W1 = W₂ = W₃
c)W1 < W₂ < W₃
d)W₂ >W1 >W₃
Ans.(b) The gravitational field is a conservative field.In a conservative field , the work done W does not depend on the path (from A to B). It depends on initial and final points W₁=W₂ = W₃

10.A particle is acted by a force F=kx, where k is a +ve constant. Its potential energy at x=0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x ?[2004]

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12.A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

a) 4.50 J b) 7.50 J
c) 5.06 J d) 14.06 J
Ans.

Multiple Choice with ONE or More Than ONE correct answers
13.A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to [1984-2 marks]

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14.A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table.If g is acceleration due to gravity, the work required to pull the hanging part on to the table is [1985-2 marks]
a) MgL b) MgL/3
c) MgL/9 d) MgL/18
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15.A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that[1987-2 marks]
a)its velocity is constant
b)its acceleration is constant
c)its kinetic energy is constant
d)it moves in a circular path
Ans.(c), (d) It is a case of uniform circular motion. Velocity and acceleration keep on changing th eir directions. Their magnitudes remain constant. Kinetic energy remains constant.Options (c) and (d) are correct.

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17.A small ball starts moving from A over a fixed track as shown in the figure. Surface AB has friction. From A to B the ball rolls without slipping. Surface BC is frictionless. K_A, K_B and K_c are kinetic energies of the ball at A,B and C respectively. Then [2006-5 marks]

a)h_A > h_c;K_B > K_{c b) h_A > h_c;K_B > K_c}
c)h_A = h_c;K_B = Kc d)h_A < h_c;K_B > K_c
Ans.

Comprehension based questions
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g=10 m/s²)

18.The speed of the block at point B immediately after it strikes the second incline is

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19.The speed of the block at point C, immediately before it leaves the second incline is

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20.If the collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

Ans.(c) The velocity of the block coming down from the incline AB makes an angle 30° with the incline BC. If the block collides with the incline BC elastically, the angle of velocity of the block after collision with the incline shall be 30°.Hence just after collision with the incline BC the velocity of block shall be horizontal. So immediately after the block strikes the second incline, its vertical component of velocity will be zero.

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22.A pulley arrangement is shown in the figure. The cylinder A has a diameter of 30cm and the cylinder B has a diameter of 20cm. The working handle has an arm of 50cm. The direction of winding of the rope on A is opposite to that on B. Calculate the mechanical advantage of this arrangement. [1980]

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23.A body of mass 2kg is being dragged with a uniform velocity of 2m/s on a rough horizontal plane. The co-efficient of friction between the body and the surface is 0.20, J=4.2 joule/calorie and g = 9.8m/s². Calculate the amount of heat generated in 5 second. [1980-5 marks]
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24.In the figures (a) and (b), AC, DG and GF are fixed inclined planes, BC = EF = x and AB = DE = y. small block of mass is released from the point A. It slides down AC and reaches C with a speed v_c. The same block is released, from rest, from the point D. It slides down DGF and reaches the point F with speed v_F. The co-efficients of kinetic frictions, between the block and both the surfaces AC and DGF, are u Calculate v_c and v_F.[1980-6 marks]

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25.A lead bullet just melts when stopped by an obstacle. Assuming that 25 percent of the heat is absorbed by the obstacle, find the velocity of the bullet. Its initial temperature is 27°C .(Melting point of lead = 327° C, specific heat of lead = 0.03 calorie/g°C, latent heat of fusion of lead = 6 cal/g° C, J = 4.2 joule/calorie).[1981-3 marks]
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26.Two blocks A and B are connected to each other by a string and a spring; the string passes over a frictionless pulley as shown in the figure. Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed.

The co-efficient of friction between the surfaces of blocks is 0.2. Force constant of the spring is 1960 newton/m. If mass of block A is 2kg, calculate the mass of block B and the energy stored in the spring. [1982-5 marks]
Ans.Both A and B are moving with uniform speed. Their acceleration is zero and so the force on them should be zero. The spring is loaded. Let the extension of the spring be x. The force acting on the spring is the tension T. The tension T is set up in the string. Free body diagrams of B, spring and A are shown in the figures.

27.A 0.5 kg block slides from the point A ( see fig) on a horizontal track with an initial speed of 3 m/s towards a weightless horizontal spring of length 1 m and force constant 2 newton/m. The part AB of the track is ffictionless and the part BC has the coefficients of static and kinetic friction as 0.22 and 0.2 respectively. If the distances AB and BD are 2 m and 2.14 m respectively, find the total distance through which the block moves before it comes to rest completely. (Take g = 10 m/s²).[1983-7 marks]

Ans.The part AB of the track is frictionless. Hence no energy is lost along AB. The 0.5 kg block travels to spring and compresses the spring by an amount x. Energy is stored in the spring. Kinetic energy of block = Workdone against kinetic friction + potential energy of spring

28.A string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass M = 2 kg attached to it at a distance of 1 m from the wall. A mass m = 0.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed with which the mass M will hit the wall when the mass m is released? [1985-6 marks]

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29.A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see figure). The small sphere A

Ans.

30.A block of mass 0.18 kg is attached to a spring of force-constant 2N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is [2011]

Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Physics Electrostatics Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Electrostatics Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Electrostatics Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volt. The potential at the centre of the sphere is [1983- Imark]
a) zero b) 10 volt
c)same as at a point 5 cm away from the surface
d)same as at a point 25 cm away from the surface
Ans.(b) Electric potential at any point inside a hollow metal sphere is constant. The potential at the surface is 10 volt. The potential at the centre will also be 10

2.Two point charges +q and -q are held fixed at (-d,0) and (d,0) respectively of a x-y coordinate system. Then [1995-2 marks]
a)The electric field E at all points on x-axis has the same direction
b)Electric field at all points on y-axis is along x-axis
c)Work has to be done in bringing a test charge from infinity to the origin
d)The dipole moment is 2qd along the x-axis
Ans.(b) (a) E on x-axis E will not have same direction along entire x-axis. Option (a) is incorrect.

For – d < x < d, the field is along +x-axis For all other points, E is along negative x-axis
b)Electric field at P, a point on y-axis is parallel to x-axis. It is not along x-axis itself. It is nearest to correct answer.
c)Electric potential at origin is zero No work has to be done in bringing a test charge from infinity to the origin. Option (c) is incorrect
d)The dipole moment is directed from -q charge to +q charge, along negative direction, of x-axis.
.•. Dipole moment = -2qd along x-axis.
The option is incorrect.Hence option (b) is nearest to correct answer.

3.A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to a potential difference 2V. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is [1995-2 marks]

Ans.

4.An electron of mass m_e, initially at rest, moves through a certain distance in a uniform electric field in time t_r A proton of mass m_p) also initially at rest, takes time t₂ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t, /1, is nearly equal to[1997-1 mark]
a) 1 b) (m_p/m_e)^1/2
c) (m_e/m_p)^1/2 d) 1836
Ans.

Ans.

Ans.(d) Resistor (R) and capacitor (C) are connected in parallel. They are connected across a 1.5 volt source of negligible resistance.Since the capacitor is directly connected to voltage source and there is no resistance in the path,

7.Two identical metal plates are given positive charges Q1 and Q₂ (<Q₁) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is [1999-2 marks]
a) (Q1+Q₂)/(2C) b) (Q₁+Q₂)/C
c)(Q1-Q₂)/C d) (Q₁-Q₂)/(2C)
Ans.

8.For the circuit shown in figure, which of the following statement is true ? [ JEE ’99, 2 ]
a)with S1 closed, V1 = 15 V, V₂ = 20 V
b)with S₃ closed, V₁ = V₂ = 25 V
c)with S1 & S₂ closed, V₁ = V₂ = 0
d)with S1 & S₃ closed, V1 = 30 V, V₂ = 20 V
Ans.(d) No change of any potential across any capacitor will occur unless the two capacitors Cj and C₂ are either connected in series or in parallel.Charges would be maintained as they are unless Sj, S₂ and S₃, all are closed.This condition is given in none of the options. Hence the potentials of C1 and C₂ will be maintained as V1 = 30 volt and V₂ = 20 volt, with S, and S₃closed.

9.Three charges Q, -i-q and -t-q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero

Ans.

10.A parallel plate capacitor of area A, Plate separation d and capacitance C is filled with three different dielectric materials having dielectric constant K_pK₂ and K₃ as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by

Ans.

11.Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in [JEE 2001-1 mark]

Ans.(c) Electric lines of force do not end at positive charge as shown in (a). The option is therefore incorrect. Electric lines of force never form a closed loop. Options (b) and (d) are incorrect.Option (c) represents correct answer. Mutual repulsion between similar charges is depicted in figure.

12.Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is [2001-1 mark]

Ans.(a) Due to attraction of positive charge, the negative charge is bound and so it will not flow to capacitor B through the switch S.Option (a) represents the correct answer.

13.A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x=+l cm and C be the point on the y-axis at Y=+l cm. Then the potentials at the points A,B and C satisfy. [2001-1 mark
a)V_A<V_B b)V_A>V_{B c)}V_A<V_c d)V_A>V_c
Ans.(b) Potential decreases as we move along the direction of electric field. The field E is uniform and runs patallel to x-axis.Any line perpendicular to x-axis is an equipotential line.

14.Two equal point charges are fixed at x = -a and x = +a on the axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to [JEE 2002-1 mark]
a)x b) x² c) x³ d) 1/x
Ans.

15.Two identical capacitors, have the same capacitance C. One of them is charged to potential Vj and the other V₂. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is[JEE 2002 (Scr), 3]

Ans.(c) When two capacitors joined together by connecting positive plate to positive plate and negative plate to negative plate, then the loss of mechanical energy or heat produced or work done to drive the change is given by

16.A metalic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force? [JEE’2003 (scr)]

Ans.(c) Field lines do not enter the metallic portion of the shell as field is zero inside the metal. Hence options (a) and (d) are incorrect.The field lines are normal to metal surface.Hence option (b) is incorrect.Both the conditions are satisfied in option (c), Hence (c) represents the correct answer.

17.Six charges of equal magnitude , 3 negative are to be placed on PQRSTU comers of a regular hexagon, such that field at the centre is double that of what it would have been if only one +ve charge is placed at R. [2004-1 mark]

Ans.

(c) According to option (c), the electric fields at O due to
i)P and S nullify each other
ii)Q and T nullify each other
iii)R and U add up to 2E
Hence option (c) represents the answer.

18.A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be [2004-1 mark]

Ans.(d) At any point over the spherical Gaussian msurface, net electric field is the vector sum of electric fields due to all the three charges +q_p -q1 and q₂.

19.Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is [2005-1 mark]

Ans.(c) All the three charge sheets will produce electric field at P. The field will be along negative Z-axis.Hence

20.Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then. [2007-3 marks]
a)negative and distributed uniformly over the surface of the spher
b)negative and appears only at the point on the sphere closest to the point charge
c)negative and distributed non-uniformly over the entire surface of the sphere
d)zero
Ans. (d) When a positive point charge is placed outside a conducting sphere, a rearrangement of charge take place on the surface.But the total charge on the sphere is zero as no charge has left or entered the sphere.

21.A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. [2007-3 marks]
a)A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
b)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
c)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
d)No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
Ans.(a) When a charge density is given to the inner cylinder, the potential developed at its surface is
different from that on the outer cylinder. This is because the potential decreases with distance for a
charged conducting cylinder when the point of consideration is outside the cylinder.
But when a charge density is given to the outer cylinder, it will change its potential by the same amount as that of the inner cylinder. Therefore no potential difference will be produced between the cylinders in this case.

22.A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is [2007-3 marks]

a)zero everywhere
b)non-zero and uniform
c)non-uniform
d)zero only at its center.
Ans.

Ans.It can be seen that potential at both points A and B are zero. When the charge is moved from A to B, work done by the electric field on the charge will be zero.

Ans.

25.A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K=2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is [2008]

Ans

Ans.

27.Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s). (2009)
a)The angular momentum of the charge -q is constant
b)The linear momentum of the charge -q is constant
c)The angular velocity of the charge -q is constant
d)The linear speed of the charge -q is constant
Ans.(a) The angular momentum of the charge -q is constant

28.A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ±a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is(2009)

Ans.

29.Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q₁ Q₂, Q₃, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then the ratio of the charges given to the shells, Q₁ : Q₂: Q₃, is (2009)
a)1 : 2 : 3 b) 1 : 3 : 5 c) 1 : 4 : 9 d) 1 : 8 : 18
Ans.

Ans.

Multiple Choice with ONE or More Than ONE correct answers
32.Two equal negative charge -q are fixed at points (0, -a) and (0, a) on y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will. [1984-2 marks]
a)execute simple harmonic motion about the origin
b)move to the origin remain at rest
c)move to infinity
d)execute oscillatory but not simple harmonic motion.
Ans.

33.A parallel plate air capacitor is connected to a battery. The quantites charge, voltage, electric field and energy associated with this capacitor are given by Q₀,V₀,E₀ and U₀ A dielectric slab is now introduced to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q, V< E and U are related to the previous one as [1985-2 marks]
a)Q >Q₀ b) V > V₀ c) E >E₀ d)U>U₀
Ans.

34.A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to [1987-2 marks]

Ans.

35.A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles [1987-2 marks]
a)the charge on the capacitor increases
b)the voltage across the plates increases
c)the capacitance increases
d)the electrostatic energy stored in the capacitor increases.
Ans.

36.A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -3Q, the new potential difference between the same two surfaces is [1989-2 marks]
a) V b) 2V c) 4V d) -2V
Ans.

Ans.

38.A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q,E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and the workdone on the system, in question, in the process of inserting the slab, then [1991-2 marks]

Ans.

39.Two identical thin rings, each of radius R metre, are coaxially placed at a distance R metre apart. If Q1 coulomb and Q₂ coulomb, are respectively the charges uniformly spread on the two rings, the work done in moving charge q from the centre of one ring to that of the other is [1992-2 marks]

Ans.

40.The magnitude of electric field E in the annular region of a charged cylindrical capacitor
a)Is same throughout [IIT’96, 2]
b)Is- higher near the outer cylinder than near the inner cylinder
c)Varies as (1/r), where r is the distance from axis
d)Varies as (1/r²), where r is the distance from axis
Ans.

41.A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s)

Ans.(d) The lines of force never enter a metallic sphere because intensity is zero inside a conductor/metal. Hence options (b) and (c) are incorrect.The lines of force are at normal to the surface. Hence option (a) is incorrect.Option (d) represents the correct answer.

42.A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x=0 and positive plate is at x=3d. The slab is equidistant from the plates. The capacitor is given some charge. As one goes from 0 to 3d, [1998-2 marks]
a)the magnitude of the electric field remains the same
b)the direction of the electric field remains the same
c)the electric potential increases continuously
d)the electric potential increases at first, then decreases and again increases.
Ans.b)The direction of electric field remains the same. Option (b) is therefore correct.
c)Electric field lines always flow from higher potential to lower potential. The electric potential V, therefore, increases continuously as one goes from x = 0 to x = 3d. OA || BC Slope of (OA) > slope of AB Option (c) is correct.
d)The option is incorrect. Refer to figure (iii)

Ans.

Ans.(c), (d) Points A and B lie on the ellipsoidal cavity carved within a perfect conductor. Since the

potential of all points which lie on the conductor,is same,the potentials at A and B are same.
Potential at A=Potential at B Option (c) is correct.According to Gauss theorem,Hence option (d) is correct.Options (a) and (b) are incorrect as the cavity is ellipsoidal. It may, however, be noted that options (a) and (b) hold good in case of a spherical caivty.

47.spherical symmetric charge system is centred at origin. Given, electric potential [2006-5 marks]

Ans.

48.A few electric field for a system of two charges Q, and Q₂ fixed at two different points on the x-axis are shown in the figure. These lines susggest that

Ans.(a), (d) Number of lines of force is directly pro- portional to the magnitude of the charge so |Qi|>|Q₂|
At null point where E = 0, there will be no lines of force of only the given two charges are considered, there is a chance of getting E = 0 to the right of Q₂ (Null point will be closer to the charge having small magnitude)

49.A spherical metal shell A of radius R_A and a solid metal sphere B of radius R_B (<R_A) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. (2011)

Ans.

50.Which of the following statement(s) is / are correct
a)If the electric field due to a point charge varies as r^{2 5} instead of r², then the Gauss law will still be valid (2011)
b)the gauss law can be used to calculate the field distribution around an electric
c)If the electric field between two point charges is zero some where, then the sign of the two charges is the same
d)the work done by the external force in moving a unit positive charge from point A at potential V_Ato potential V_B is (V_B – V_A)
Ans.

Assertion – Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-1 and2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase d) Statement-1 is false, statement-2 is true.

51.Statement -1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
Statement -2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the

Ans.(b) Statement -1 is true, you all are familiar with this convention.Statement – 2 is true. You all know this, recall the shell theorem.But statement -2 is not the correct explanation of statement – 1.

Comprehension based question
Read the passage given below and answer the questions that follow
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

52.The electric field at r = R is
a) independent of a b) directly proportional to a c) directly proportional to a² d) inversely proportional to a
Ans.(a) Electric field at a distance R from the centre of the nucleus es,

Ans.

54.The electric field within the nucleus is generally observed to be linearly dependent on r. This implies
a)a=0 b)R/2 c)a=R d)2R/3
Ans.

Matching type
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column – II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (Potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and p be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. [2009]

Ans.

56.A rigid insulated wire frame in the form of a right angled triangle ABC, is set in a vertical plane as shown in fig. Two beads of equal masses m each and carrying charges qj and q₇ are connected by a cord of length / and can slide without friction on the wires.Considering the case when the beads are stationary determine [1978]
Ans.(a) Consider first the equilibrium of bead at P, having charge q_r Different forces acting on it are shown in the figure. If the charges qj and q₂ are similar in nature, then electric force F will be repulsive and is given by

57.A charged particle is free to move in an electric field. Will it always move along an electric line of force? [1979]
Ans.It moves along the line of force only if it is straight.

58.A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal. Find the potential at the common centre. [1981-3 marks]
Ans.

59.The figure shows two identical parallel plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant (or relative permittivity) 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

Ans.

Ans.The moving charge -q has potential and kinetic energies while at C and at D. The sum of the two energies at C and D remains constant.

61.Three point charges q, 2q and 8q are to be placed on a 9 cm long straight line. Find the positions where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the position of the charge q due to the other two charges? [1987-7 marks]
Ans.The potential energy will be minimum when the two bigger charges are located at maximum distance in the system. Let x cm = x x 10-²m, be the distance between 2q and q.

62.Three particles, each of mass lg and carrying a charge q, are suspended from a common point by insulated massless strings, each 100 cm long. If the particles are in equilibrium and are located at the comers of an equilateral triangle of side length 3cm, calculate the charge q on each particle. (Take g = 10m/s²) [1988-5 marks]
Ans.Each particle of mass m and charge q is suspended by a 100 cm long string, m=l gram. They are located at corners of an equilateral triangle of sidelength 3 cm. Three forces act on each particle.

Ans.

64.Two fixed charges -2Q and Q are located at the points with coordinates (-3a, 0) and (+3a, 0) respectively in the x-y plane. [1991-4+2+2 marks]
a)Show that all points in the x-y plane, where the electric potential due to the two charges is zero, lie on a circle. Find its radius and the location of its centre.
b)Give the expression V(x) at a general point on the x-axis and sketch the function V(x) on the whole x-axis
c)If a particle of charge +q starts from rest at the the centre of the circle, show by a short quantitative argument that the particle eventually crosses the circle. Find its speed when it does so.
Ans.Charge (-2Q) is located at (-3a, 0) in x-y plane Charge (Q) is located at (+3a, 0) in x-y plane, a) Locus of zero potential:Let P be a general point, denoted by (x,y), wher potential due to the two charges is zero.

65.a) A charge of Q coulomb is uniformly distributed over a spherical volume of radius R metre. Obtain an expression for the energy of the system.
b)What will be the corresponding expression for the energy needed to completely disassemble the planet earth against the gravitational pull amongest its constituent particles?
Assume the earth to be a sphere of uniform mass density. Calculate this energy, given the product of the mass and the radius of the earth to be 2.5 x l0³¹kg.m.
c)If the same charge of Q coulomb as in part a) above is given to a spherical conductor of the same radius R, what will be energy of the system? [1992-10 marks]
Ans.

66.Two parallel plate capacitors A & B have the same separation d = 8.85 x 10^-4 m between the plates. The plate area of A & B are 0.04 m² & 0.02 m²respectively. A slab of di-electric constant (relative permittivity) K=9 has dimensions such that it can exactly fill the capacitor between the plates of [1999-7]
i)the di-electric slab is placed inside A as shown in the figure (a) A is then charged to a potential difference of 110 volt. Calculate the capacitance of A and the energy stored in it.
ii)the battery is disconnected & then the di-electric slab is moved from A . Find the work done by the external agency in removing the slab from A
iii)the same di-electric slab is now placed inside B, filling it completely. The two capacitors A & B are then connected as shown in figure (c). Calculate the energy stored in the system.

Ans.

Ans.

68.Two square metal plates of 1 m side are kept 01 m apart, like a parallel plate capacitor, in air in such a way that one of their edges is perpendicular, to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of e.m.f. 500 volt . The plates are then lowered vertically into the oil at a speed of 0.001 m/s. Calculate the current drawn from the battery during the process, [di-electric constant of oil = 11, E₀ = 8.85 x 10-¹² C²/N¹ m¹] [JEE ’94, 6]
Ans.As here battery remains attached to the circuit V=constant. Now as due to lowering of plates in the oil, capacity will increase gradually and as q=CV the charge on capacitor will increase. This gradual increase in q results in current drawn from the battery.If at any instant, y length of plate is dipped in oil, the system will be equivalent to two capacitors in parallel, one with air and the other with oil as dielectric so that

69.The capacitance of a parallel plate capcitor with plate area ‘A’ & separation d is C. The space between the plates is filled with two wedges of di-electric constants. K_t & K₂ Find the capacitance of the resulting capacitor. [JEE’96,2]
Ans.

70.Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density a . The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere. [1996-3 marks]
Ans.

71.Two capacitors A and B with capacities 3 mF and 2 mF are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in the figure with one wire from each capacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2 mF capacitor C with lead wires falls on the free ends to complete the circuit. Calculate [ JEE ’97 -5 marks]
i)the final charge on the three capacitors and
ii)The amount of electrostatic energy stored in the system before and after the completion of the circuit.

Ans.

72.A conducting sphere S1 of radius r is attached to an insulating handle . Another conducting sphere S₂ of radius R is mounted on an insulating stand. S₂ is initially uncharged . S1 is given a charge Q, brought into contact with S₂ & removed, S1 is recharged such that the charge on it is again Q & it is again brought into contact with S₂ & removed. This procedure is repeated n times.[1998-8 marks]
a)Find the electrostatic energy of S₂ after n such contacts with S₁
b)What is the limiting value of this energy as n->infinity?
Ans.When a conducting sphere S, is brought in contact with another conducting sphere S₂, a transfer of charge occurs from higher potential to lower potential till the two spheres attain equal potential. Let S1 contain charge Q before contact with S₂. On contact, let a charge q shift from S1 to S₂

Ans.

Ans.Let the particle be, at some instant, at a point P distant x from the origin. Of the four charges placed along y-axis, the like charges repel each other while the unlike charges attract each other. At some value of x, the attractive and repulsive forces balance each other. Therefore the attractive forces will move the charge towards origin.

75.Charges +q and -q are located at the comers of a cube of side a as shown in the figure. Find the work done to separate the charges to infinite distance. [JEE 2003-2 marks]

Ans.

Ans.(a) The free dipole, far away from the origin, travels towards origin, where a charge (+Q) is fixed. There will be a decrease in the electrostatic potential energy of the dipole. This will be equal to kinetic energy of the dipole. When the dipole is at a distance d from origin,

Ans.

78.A conducting liquid bubble of radius a and thickness t (t << a) is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet. [2005-2 marks]

Ans.A liquid-bubble contains air inside and liquid in the outside surface. When the bubble collapses into a droplet, the volume of liquid remains same in the transformation.

Ans.

True / False type
81.The work done in carrying a point charge from one point to another in an electrostatic field depends on the path along which the point charge is carried. [1981-2 marks]
Ans. False. Electrostatic force is conservative in nature. Work done in carrying a charge between two points does not depend upon path’ along which the charge is carried.The statement is false.

82.Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge Q coulomb and the other an equal
Ans.True.The metallic sphere which acquires positive charges loses electrons and so it loses mass. The metallic sphere which gains negative chage gains electrons and so it gains mass. Their masses on charging are evidently different.The statement is true.

83.A small metal ball is suspended in a uniform electric field with the help of an insulated thread. If high energy X-ray beam falls on the ball, the ball will be deflected in the direction of the field.[1983-2 marks]
Ans.True.When a high energy X-ray beam falls on a metal ball, it ejects electrons from the ball. The ball therefore becomes positively charged and gets deflected in the direction of electric field.The statement is true.

84.Two protons A and B are placed in between the two plates of a parallel plate capacitor charged to a potential difference V as shown in the figure. The forces on the two protons are identical.[1986-3 marks]

Ans.True.When a parallel plate capacitor is charged to a potential difference V, a uniform electric field E-V / Jis produced between the plates. Let each of the proton, A and B, carry charge q.Force on a proton, A or B=qE Since q and E are same for each proton, the forces on them are identical.The statement is true

85.A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the centre of the ring and released from rest. The particle executes a simple harmonic motion along the axis of the ring. [1988-2 marks]
Ans.

The force is not proportional to displacement. The charge particle will not execute simple harmonic motion.The statement is false.Note : If x<< R, the charged particle will execute simple harmonic motion.

86.An electric line of force in the x-y plane is given by the equation x² + y² = 1. A particle with unit positive charge, initially at rest at the point x = l,y = 0 in the x-y plane, will move along the circular line of force. [1988-2 marks]
Ans.

A unit positive charge is placed at A(1,0).Line of force is circular with radius =1.A line of force represents the path in an electric field along which a unit positive charge moves. The unit positive charge at A is already on the circular line of force. It will move along the circular line of force.The statement is true.

Fill in the blanks type
87.Five identical capacitor plates, each of area A, are arranged such that adjacent plates are at a distance d apart. The plates are connected to a source of emf V as shown in the figure.The charge on plate 1 is ……………. and on plate 4 is [1984-2 marks]

Ans.Plates 1 and 2 form a parallel plate condenser. Plate 1 is connected to +ve terminal while plate 2 is connected to negative terminal.

88.Figure shows line of constant potential in a region in w’hich an electric field is present. The values of the potential are written in brackets Of the points A,B and C, the magnitude of the electric field is greatest at the point………[1984-2marks]

Ans.The magnitude of electric field is greatest at the point where the lines of force are crowded most, being close to each other. At B, the separation between 10V and 20 V lines is the least, as is clear from the figure.Hence the electric field is greatest at B.

89.Two small balls having equal positive charge Q (coulomb) on each are suspended by two insulating strings of equal length L(metre) from a hook fixed to a stand. The whole setup is taken in a satellite into space where there is no gravity (state of weightlessness). The angle between the two strings is ………….. and the tension in each string is……… ….newton.[1986-2 marks]

Ans.The two balls hang in gravity-free space in state of weightlessness in the satellite. There is only electrostatic force of repulsion between them. The balls will be repelled till the two strings are at 180°. The tension in each string will be equal to the electrostatic force between charges.

90.Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region beween the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes…………………[1989-2 marks]
Ans.

91.A point charge q moves from point P to point S along the path PQRS (figure) in a uniform electric field E pointing parallel to the positive direction of the X-axis. The coordinates P,Q,R and S are (a,b,0), (2a,0,0), (a,b,0) and (0,0,0) respectively. The work done by the field in the above process is given by the expression [1989-2 marks]

Ans.

92.The electric potential V at any point x,y,z (all in metre) in space is given by V = 4x² volt. The electric field at the point (lm, 0, 2m) is………………. V/m [1992-1 mark]
Ans.

93.Five point charges, each of value +q coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on the point charge of value -q coulomb placed at the centre of the hexagon is …. newton [1992-1 mark]
Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Physics Heat And Thermodynamics Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Heat And Thermodynamics Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Heat And Thermodynamics Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.A constant volume gas thermometer works on [1980]
a)the principle of Archimedes
b)Boyle’s law
c)Pascal’s law
d)Charle’s law
Ans.(d)

2.A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36° C The temperature difference across the layer A is [1980]
a) 6°C b) 12°C
c) 18°C d) 24°C
Ans.

3.An ideal monoatomic gas is taken round the cycle ABCDA as shown in the P-V diagram (see figure). The workdone during the cycle is [1983-1 mark]

a) PV
b)2 PV
c)PV/2
d)Zero
Ans.

4.From the following statements, concerning ideal gas at any given temperature T, select the correct one (s). [1995-2 marks]
a)The co-efficient of volume expansion at constant pressure is the same for all ideal gases
b)The average translational kinetic energy per molecule of oxygen gas is 3kT, k being Boltzmann constant
c)The mean-free path of molecules increases with increase in the pressure
d)In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different
Ans.

Ans.

6.Two metallic sphere S1 and S₂are made of the same material and have got identical surface finish. The mass of S1 is thrice that of S₂. Both spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S₂ is [1995-2 marks]

Ans.

7.The average translational kinetic energy and the root mean square speed of molecules in a sample of oxygen gas at 300 K are 6.21 x 10-²¹J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour) [1997-1 mark]
a)12.42 x10^-21J,968 m/s
b)8.78 x 10^-21J,684 m/s
c)6.21 x 10^-21 J,968 m/s
d)12.42 x 10^-21J,684 m/s
Ans.

8.The intensity of radiation emitted by the Sun has its maximum value at a wavelength of 510 nm and that emitted by the North star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperatures of the Sun and the North Star is [1997-1 mark]
a) 1.46 b) 0.69 c) 1.21 d) 0.83
Ans.

9.The average translational kinetic energy of 0₂(molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of N₂ (molar mass 28) molecules in eV at the same temperature is [1997-1 mark]
a) 0.0015 b) 0.003 c) 048 d) 0.768
Ans.

10.A vessel contains 1 mole of 0₂ gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (relative molar mass 4) at a temperature 2 T has a pressure of [1997-1 mark]
a) P/8 b) P c) 2P d) 8P
Ans.

11.A spherical black body with a radius of 12 cm radiates 450 W power at 500 K . If the radius is halved and the temperature doubled, the power radiated in watt would be : [1997-1 mark]
a) 225 b) 450 c) 900 d) 1800
Ans.

12.One mole of a monoatomic gas is heated at a constant pressure of 1 atmosphere from OK to 100K. If the gas constant R=8.32 J/mol K, the change in internal energy of the gas is approximately [1998]
a) 2.3J b) 46J
c) 8.67×10³J d) 1.25xl0³J
Ans.

13.An ideal gas heat engine is operating between 227°C and 127°C . It absorbs 10⁴J of heat at the higher, temperature. The amount of heat converted into work is [1998]
a) 2000J b) 4000J c) 8000J d) 5600J
Ans.

14.A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [1999-2 marks]
a) 4RT b) 15RT c) 9RT d) 11RT
Ans.

15.The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300K is [1999-2 marks]

Ans.

16.Two monoatomic ideal gases 1 and 2 of molecular masses M1 and M₂ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]

Ans.

17.A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If L₃and L₂ are the lengths of the gas column before and after expansion respectively, then T1/T₂ is given by [2000-2 marks]

Ans.

18.A block of ice at – 10°C is slowly heated and converted to steam at 100°C. Which of the following curves represents the phenomen on qualitatively?[2000-2 marks]

Ans.

Ans.

20.Starting with the same gas expands from volume V_t to V₂ in three different ways. The work done by the gas is if the process is purely isothermal, W₂ if purely isobaric and W₃if purely adiabatic. Then [2000]
a) W₂ > W1 > W₃ b) W₂ > W₃ > W1
c) W₁ > W₂ > W₃ d) W1 > W₃ > W₂
Ans.

21.The plots of intensity versus wavelength for three black bodies at temperature T_p T₂ and T₃respectively are as shown. Their temperatures are[2000-2 marks]

Ans.

22.Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be [2001-2 marks]

a)45°C
b)60°C
c)30°C
d)20°C
Ans.

23.In a given process on an ideal gas, dW = 0 and dQ < 0. Then for the gas [2001]
a)the temperature will decrease.
b)the volume will increase
c)the pressure will remain constant
d)the temperature will increase
Ans.

24.P-V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to [2001-2 marks]

a)He and O_z
b)0₂ and He
c)He and Ar
d)0₂ and N₂
Ans.

25.An ideal gas is taken through the cycle A -> B —> C —>A, as shown in the figure. If the net heat supplied to the gas in the cycle is 5J, the work done by the gas in the process C —> A is [2002-2 marks]

a)-5J
b)-10J
c)-15J
d)-20J
Ans.

26.Which of the following graphs correctly represents the variation of b = -(dV/dP)/V with P for an ideal gas at constant temperature? [2002-2 marks]

Ans.

27.An ideal black body at room temperature is thrown into a furnace. It is observed that [2002-2 marks]
a)initially it is the darkest body and at later times the brightest.
b)it is the darkest body at all times
c)it cannot be distinguished at all times.
d)initially it is the darkest body and at later times it cannot be distinguished.
Ans.(a) According to Kirchhoff’s law, good absorbers are good emitters and bad reflectors. While at lower temperature, a black-body absorbs all the incident radiations. It does not reflect any radiation incident upon it when it is thrown in the furnace. Initially it is therefore the darkest body.
At later times, the black body attains the temperature of the hot furnace and so it radiates all types of wavelengths with maximum energy. It becomes the brightest of all.Option (a) represents the answer.

28. The graph, shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivite and absorptive powers of the two bodies.

a)E_x > E_yand a_x <a_y
b)E_x < E_yand a_x >a_y
c)E_x > E_yand a_x >a_y
d)E_x <E_yand a_x <a_y
Ans.

Ans.

30.The PT diagram for an ideal gas is shown in the figure, where AC is an adiabatic process. Find the corresponding PV diagram. [2003-2 marks]

Ans.(b) An inspection of the P-T graph reveals that
1)AC is an adiabatic process (given)
2)AB is an isothermal process a T constant
3)BC is an isobaric process at P constant.
i)In all the four options, BC is an isobaric process
ii)AB is an isothermal process.
.•.pv = constant
Graph between P and V is a rectangular hyperbola of the form xy = constant.
Graphs (b) and (d) satisfy this condition Options (a) and (c) are therefore incorrect.
iii)AC is an adiabatic process (given). In P-V diagram, slope of AC> slope of AB because slope of adiabatic curve > slope of isothermal curve.
This condition is certainly not satisfied in option (d) where AC is a straight line at constant V. Here AC is an isochoric process. It is not an adiabatic process (d) is incorrect. Hence the ultimate correct process is (b).

31. 2kg of ice at -20°C is mixed with 5 kg of water at 20°C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container.It is given that the specific heats of water and ice are 1 kcal/kg°C and 0.5 kcal/kg⁰C while the latent heat of fusion of ice is 80kcal/kg°C
a)7 kg b) 6 kg c) 4 kg d) 2 kg
Ans.

32.Three discs A, B, and C having radii 2 cm, 4 cm and 6 cm respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. The power emitted by them are Q_A, Q_B and Q_c[2004-2 marks]
a)Q_a will be maximum b) Q_B will be maximum c) Q_c will be maximum d) Q_A = Q_B = Qc
Ans.

33.If liquefied oxygen at 1 atmospheric pressure is heated from 50 K to 300 K by supplying heat at constant rate, the graph of temperature vs time will be

Ans.

34.Two identical rods are connected between two One of, them is at 100°C containing water and another is 0°C containing ice. If rods are connected in parallel then the rate of melting of ice is q1g/sec. If they are connected in series then the rate is q₂. The ratio q₂/q1 is
a)2 b) 4 c) 1/2 d) 1/4
Ans.

35.An ideal-gas initially at P1, V, is expanded to P₂, V₂and then compressed adiabatically to the same volume V1 and pressure P₃. If W is the net work done by the gas in complete process which of the following is true? [2004]
a)W>0; P₃ > P1 b) W<0; P₃>P1
c) W>0; P₃<P1 d) W<0;P₃<P1
Ans.

36.Variation of radiant energy emitted by Sun, filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure.Which of the following option is the correct match ? [2005-2 marks]

a)Sun —T3 tungsten filament— T1, welding arc —T₂
b)Sun-T₂, tungsten filament— T1, welding arc—T₃
c)Sun —T₃, tungsten filament —T₂, welding arc —T₃
d)Sun —T1, tungsten filament—T₂, welding arc— T1
Ans.

37.In which of the following processes, heat convection does not take place primarly? [2005-2 marks]
a)land and sea breeze b) boiling of water
c)heating air around a furance d)warming of glass of bulb due to filament.
Ans.(d)Warming of glass of bulb due to filament is due to radiation primarily. For convection process, a medium is required which can move between two points to transfer heat. Bulb is almost evacuated to have no medium. Option (d) represents the answer.

38.A spherical body of area A and emissivity e = 0.6 is kept inside a perfectly black body. Energy radiated per second by the body at temperature T

Ans.

39.Calorie is defined as the amount of heat required to raise temperature of 1 g of water by 1°C and it is defined under which of the following conditions ? [2005-2 marks]
a)From 14.5°C to 15.5°C at 760 mm of Hg
b)From 98.5°C to 99.5°C at 760 mm of H
c)From 13.5°C to 14.5°C at 76 mm of Hg
d)From 3.5°C to 4.5°C at 76 mm of Hg
Ans.

40.Water of volume 2 litre in a container is heated with a coil of power lkW at 27°C. The lid of the container is open and energy dissipates at rate of 160 J/s. In how much time temperature will rise from 27°C to 77°C. [Given specific heat of water is 4.2 kJ/kg]
a)7 min b) 6 min 2 s
c) 8 min 20 s d) 14 min
Ans.

41.An ideal gas is expanding such that PT² = constant. The coefficient of volume expansion of the gas is[2008]
a)l/T b) 2/T c) 3/T d) 4/T
Ans.

42.At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1930 m/s. The gas is [1984-2 marks]
a)H₂ b) F₂ c) 0₂ d) Cl₂
Ans.

43.70 calorie of heat are required to raise the temperatureof 2 mole of an ideal gas at constant pressure from 30°C to 35°C.The amount of heat required (in calorie) to raise the temperature of the same gas through the same range (30°C to 35°C) at constant volume is [1985-2 marks]
a)30 b) 50 c) 70 d) 90
Ans.

44.Steam at 100°C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02kg at 15°C till the temperature of the calorimeter and its contents rises at 80°C.The mass of the steam condensed in kilogram is [1986-2 marks]
a)0.130 b)0.065 c)0.260 d)0.135
Ans.

45.Acylinder of radius R,made of a material of thermal conductivity K1, is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a materialof thermal conductivity K₂.The two ends of the combined system are maintained at two different temperatures.There is no loss of heat across the cylindrical surface and the system is in steady state.The effective thermal conductivity of the system is [1988-2 marks]
a)K_{1 +} K₂ b)K₁K₂(K₁ +K₂)
c) (K1 +3K₂)/4 d) (3K1 +K₂)/4
Ans.

Ans.

47.A real gas behaves like an ideal gas if its [2010]
a)pressure and temperature are both high
b)pressure and temperature are both low
c)pressure is high and temperature is low
d)pressure is low and temperature is high
Ans.(d) At low pressure and high temperature, the interaction between molcules approaces to zero. Therefore real gas is behaves as ideal gas.

48.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T_: , the work done in the process is [2011]

Ans.

Multiple Choice with ONE or More Than ONE correct answers
49.For an ideal gas [1989-2 marks]
a) the change in internal energy in a constant pressure process from temperature T1 to T₂ is equal to nC_v (T₂ -T1) , where C_v is the molar specific heat at constant volume and n the number of moles of the gas.
b) the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
c) the internal energy does not change in an isothermal process.
d) no heat is added or removed in an adiabatic process.
Ans.

50.When an ideal diatomic gas is heated at constant pressure ,the fraction of the heat energy supplied which increases the internal energy of the gas is
a)2/5 b)3/5 c)3/7 d)5/7
Ans.

51.Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities.Vessel A contains only 0₂,B only N₂ and C a mixture of equal quantities of 0₂ and N₂. If the average speed of the 0₂ molecules in vessel A is V1 that of the N₂molecules in vessel B is v₂, the average speed of the 0₂ molecules in vessel C is Where M is the mass of an oxygen molecule [1992-2 marks]

Ans.(b) According to Maxwell’s distribution of speed of gas, the average speed of molecules

52. An ideal gas is taken from the state A (pressure P, volume V) to the state B(pressure P/2,volume 2V) along a straight line path in the P-V diagram. Select the correct statement (s) from the following. [1993-2 marks]
a)The workdone by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm.
b)In the T-V diagram, the path AB becomes a part of a parabola.
c)In the P-T diagram ,the path AB becomes a part of a hyperbola.
d)In going from A to B ,the temperature j of the gas first increases to a maximum value and then decreases.
Ans.

Ans.

54.The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root -mean square velocity of the gas molecules is v, at 480 K it becomes [1996-2 marks]
a) 4v b) 2v c) v/2 d) v/4
Ans.

Ans.

56.A given quantity of an ideal gas is at pressure P and absolute temperature T.The isothermal bulk modulus of the gas is [1998-2 marks]
a)2|3 p b) P c)3|2 p d)2P
Ans.

57.Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K.The piston of A is free to move,while that of B is held fixed.The same amount of heat is given to the gas in each cylinder.If the rise in temperature of the gas in A is 30K, rise in temperature of the gas in B is [1998-2 marks]
a) 30K b) 18 K c) 50 K d) 42 K
Ans.

58.During the melting of a slab of ice at 273 K at atmospheric pressure [1998-2 marks]
a)positive work is done by the ice-water system on the atmosphere
b)positive work is done on the ice-water system by the atmosphere
c)the internal energy of the ice-water system increases.
d)the internal energy of the ice-water system decreases.
Ans.

59.A black body is at a temperature of 2880 K. The ‘ energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U₂ and between 1499 nm and 1500 nm is U₃. The Wien constant b = 2.88 x 10⁶ nm K. Then [1998-2 marks]
a) U1 = 0 b) U₃ = 0
c) U1 > U₂ d) U₂ > U1
Ans.

Ans.

61.A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per 0₂molecule to that per N₂ molecule is [1998-2 marks]
a)1:1 b) 1:2
c) 2:1 d) depends on the moments of inertia of the two molecules
Ans.

62.A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The coefficients of linear expansion of the two metals are a_c and a_B. On heating, the temperature of the strip goes up by DT and the strip bends to form an arc of radius of curvature R. Then R is : [1999-3 marks]
a)proportional at DT
b)inversely proportional to DT
c)proportional to |a_B – a_c|
d)inversely proportional to |a_B – a_c|
Ans.

63.Initially a black body at absolute temperature T is kept inside a closed chamber at absolute temperature T₀. Now the chamber is slightly opened to allow Sun rays to enter. It is observed that temperatures T and T₀ remains constant. Which of the following statements is/are true? [2006-5 marks]
a)The rate of emission of energy from the black body remains the same
b)The rate of emission of energy from the black body increases
c)The rate of absorption of energy by the black bo-‘-y increases.
d)The energy radiated by the black body equals he energy absorbed by it.
Ans.(a,d) From Stefan’s law, the rate of emission of energy from a black body is proportional to (T-T_o )⁴Since T and T₀remain constant, the rate of emission of energy remains the same. Since the temperature of the black body remains constant, the energy radiated by it = energy absorbed by it. Hence the correct choices are (a) and (d).

64.One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P₀. Choice the correct option(s) from the following. [2010]

Ans.

65.C_v and C_p denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then [2009]
a)C_p – C_v is larger for a diatomic ideal gas than for a mono atomic ideal gas
b)C_p + C_v is larger for a diatomic ideal gas than for a mono atomic ideal gas
c)C_p/C_v is larger for a diatomic ideal gas than for a mono atomic ideal gas
d)C_p . C_v is larger for a diatomic ideal gas than for a mono atomic ideal gas
Ans.

66.The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then, [2009]

a)the process during the path A B is isothermal
b)heat flows out of gas during the path B —>C—>D
c)work done during the path A—>B—>C is zero
d)positive work is done by the gas in the cycle ABCDA
A composite block is made of o il_____________ sl 6l
Ans.

67.slabs A, B, C, D and E of ^h“‘ different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat ‘Q’ flows only from left to right through the blocks. Then in steady state [2011]

a)heat flow through A and E slabs are same
b)heat flow through slab E is maximum
c)temperature difference across slab E is smallest
d)heat flow through C = heat flow through B + heat flow through D
Ans.

Assertion & Reasoning type
Instructions : The following question contains statement -1 (assertion) and statement -2 (reason) Of these statements, mark correct choice if
a)Statement – 1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement – 1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement – 1 is true, statement-2 is flase
d)Statement – 1 is false, statement-2 is true.

68.Statement-1: The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume. Statement-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision [2007-3 marks]
Ans.(b)

Matching Type
69.Heat given to process is positive, match the following option of column I with the corresponding option option of column II [2006-6 marks]

Ans.

70.Column I gives some devices and column II gives some processes on which the functioning of these devices depend. Match the device in column I with the processes in column II. [2007-6 marks]

Ans.

71.Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process.

Ans.

72.Column II gives certain systems undergoing a process. Column I sugests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process (es) from Column II. [2009]

Ans.p) When an uncharged capacitor is connected to a battery, it becomes charged and energy is stored in the capacitor.
q) When a gas in an adiabatic container fitted with an adiabatic piston is compressed by pushing the piston then internal energy of the system increases du = dQ – dW = O – ( Pdv) = + Pdv.
Mechanical energy provided to the system (by the moment of the piston) is converted into kE of gas molecules.
r) As the gas in a rigid container gets cooled, the internal energy of the system will decrease. The average KE per molecule will decrease. Hence None of the options in column I matches.
s) When a heavy nucleus initially at rest splits into two nuclei of nearly equal masses and some neutrons are emitted then (i) internal erergy of the system is converted into mechannical energy (ii) mass of the system decreases which converts into energy.
t) When a resistive wire loop is placed in a time varying magnetic field per pendicular to its plane, (i) Induced current shows in the loop due to which the energy of system is increased.

73.One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P.V.diagram. Column II given the characteristics involved in the cycle. Match them with each of the processes given in Column I

Ans.

Ans.

76.A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same cross-section. At 25°C» the composite rod is 1 metre in length, of which the length of the copper rod is 30cm. At 125°C the length of the composite rod increases by 1.91mm.When the composite rod is not allowed to expand by holding it between two rigid walls, it is found that the length of the two constituents do not change with the rise of temperature. Find the Young’s modulus and the coefficient of linear expansion of the second rod.[Given : Coefficient of linear expansion of copper = 1.7xI0-⁵per°C, Young’s modulus of copper 1.3×10¹¹N/m² ]
Ans.

77.A solid material is supplied with heat at constant rate. The temperature of the material is changing with the heat input as shown in the graph in figure.Study the graph carefully and answer the following questions.

i)What do the horizontal region AB and CD represent ?
ii)If CD is equal to 2AB, what do you infer?
iii)What does the slope of DE represent?
iv)The slope of OA > the slope of BC. What does this indicate ? [1980]
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78.A jar contains a gas and a few drops of water at T K .The pressure in the jar is 830 mm of Hg. The temperature of the jar is reduced by 1%. The saturated vapour pressures of water at the two temperatures are 30 and 25mm of Hg. Calculate the new pressure in the jar. [1980]
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79.A lead bullet just melts when stopped by an obstacle. Assuming that 25% of the heat is absorbed by the obstacle, find the velocity of the bullet if its initial temperature is 27°C. (Meltging point of lead = 327°C. Specific heat of lead = 0.03 cal/g°C, Latent heat of fusion of lead = 6 cal/g, J = 4.2 J/cal.) [1981-3 marks]
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80.A cyclic process ABCA shown performed with a constant mass of an ideal gas. Show the same process on a P-V diagram (In the figure, CA is ^Tl¹²parallel to the V-axis and BC is parallel to the T-axis) [1981-4 marks]

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81.Calculate the work done when one mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are 10⁵N/m²and 6 litre respectively. The final volume of the gas is 2 litre. Molar specific heat of the gas at constant volume is 3R/2. [1982-8 marks]
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82.A solid sphere of copper of radius R and a hollow sphere of the same material of inner radius r and outer radius R are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster? [1982-2 marks]
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83.One gram mole of oxygen at 27°C and one atmospheric pressure is enclosed in a vessel.
i)Assuming the molecules to be moving with v_nns, find the number of collisions per second which the molecules make with one square metre area of the vessel wall.
ii)The vessel is next thermally insulated and moved with a’constant speed v₀. It is then suddenly stopped. The process results in a rise of the temperature of the gas by 1°C. Calculate the speed v₀. [1983-8 marks]
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Ans.

Workdone is negative as the volume in right chamber decreases.

85.Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0°C and a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at 62°C. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.[1985-6 marks]
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86.An electric heater is used in a room of total wall area 137m² to maintain a temperature of +20°C inside it, when the outside temperature is -10°C. The walls have three different layer materials. The innermost layer is of wood of thickness 2.5cm, the ‘ middle layer is of cement of thickness 0 cm and the outermost layer is of brick of thickness 25.0 cm. Find the power of the electric-heater. Assume that there is no heat loss through the floor to the ceiling. The thermal conductivities of wood, cement and brick are 0.125, 1.5 and 1.0 watt/m°C respectively. [1986-8 marks]

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89.An ideal mono atomic gas is confined in a cylinder by a spring-loaded piston of cross-section 8.0 x l0^_³m² Initially the gas is at 300 K and occupies a Volume of 2.4 x 10^_³m³ and the spring is in its relaxed (un stretched, uncompressed) state, The gas is heated by a small electric heater until the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied (in joule) by the heater. The force constant of the spring is 800QN/m, atmospheric pressure is 1.0×10-⁵Nm-². The cylinder and the piston are thermally insulated. The piston is massless and there is no friction between the piston and cylinder. Neglect heat loss through lead wires of the heater. The heat capacity of the heater coil is negligible. Assume the spring to be mass less.

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90.An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2.
i)How many degrees of freedom do the gas molecules have?
ii)Obtain the work done by the gas during the expansion as a function of the initial pressure P and volume V. [1970-7 marks]
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91.Three moles of an ideal gas(Cp=7/2 R) at pressureP_A and temperature T_A are isothermally expanded to twice the initial volume. The gas is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure P_A.[1991-4+4 marks]
a)Sketch P-V and P-T diagrams for the complete processb)
b)Calculate the net workdone by the gas, and the net heat supplied to the gas during the complete process.

92.Two moles of the helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal, calculate the following quantities in this process :

a)The net change in the heat energy
b)The net work done
c)The net change in internal energy [1992-8 marks]
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93.A cylindrical block of length 0.4m and area of cross section 0.04 m² i^s placed coaxially on a thin metal disc of mass 0.4 kg and the same cross-section. The upper face of the cylinder is maintained at a constant temperature of 400K and the initial temperature of the disc is 300K. If the thermal conductivity of the material of the cylinder is 10 watt/mK and the specific heat of the material of the disc is 600J/kgK, how long will it take for the temperature of the disc to increase to 350K? Assume, for purpose of calculation, the thermal conductivity of the disc to be very high and the system to be thermally insulated except for the upper face of the cylinder. [1992-8 marks]
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94.One mole of a monoatomic ideal gas is taken through the cycle shown in figure.

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95.An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are Q1 = 5960 J , Q₂ = -5585 J , Q₃ =-2908 J and Q₄ = 3645 J, respectively. The corresponding quantities of work involved are W1 = 2200 J, W₂ = -825 J, W₃ = -1100 J, and W₄
i)Find the value of W₄
ii)What is the efficiency of the cycle?
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96.A closed container of volume 0.02 m³ contains a mixture of neon and argon gases, at a temperature of 27° C & pressure of 1 x 10⁵ Nnr² . The total mass of the mixture is 28 g. If the molar masses of neon and argon are 20&40 g mol¹ respectively , find the masses of the individual gases in the container, assuming them to be ideal. [Universal gas constant R = 8.314 J/mol K ] [JEE ’94, 6]
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97.A gaseous mixture enclosed in a vessel of volume V consists of one mole of a gas A with g( = Cp/Cv)=5/3 & another gas B with g =7/5 at a certain temperature T. The molar masses of the gases A & B are 4 & 32 respectively. The gases A &B do not react with each other and are assumed to be ideal. The gaseous mixture follows the equation; py^19/13 = const, in adiabatic processes.[1995-10 marks]
a)Find the number of moles of the gas B in the gaseous mixture.
b)Compute the speed of sound in the gaseous mixture at T = 300 K.
c)If T is raised by 1 K from 300 K, find the percentage change in the speed of sound in the gaseous mixture.
d)The mixture is compressed adiabatically to 1/5 of its initial volume V . Find the change in its adiabatic compressibility in terms of the given quantities.
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98.At 27°C two moles of an ideal monoatomic gas occupy a volume V. The gas expands adiabatically to a volume 2V. Calculate i) the final temperature of the gas, ii) change in its internal energy, and iii)the work done by the gas during this process.[1996-5 marks]
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99.The temperature of 100 gm of water is to be raised from 24° C to 90° C by adding steam to it. Calculate the mass of the steam required for this purpose. [1996-2 marks]
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100.A thin rod of negligible mass and area of cross section 4 x l0^_⁶m², suspended vertically from one end, has a length of 0.5 m at 100°C. The rod is cooled to 0°C, but prevented from contracting by attaching a mass at the lower end. Find i) this mass, and ii) the energy stored in the rod. Given for the rod, Young’s modulus =10¹¹N/m², coefficient of linear expansion = 10-^{5 K-⁵}and g = 10m/s²[1997-5 marks]
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101.A double pane window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m² and thickness 0.01 m separated by a 0.05m thick stagnant air space. In the steady state, the room glass interface and the glass outdoor interface are at constant temperatures of 27°C and 0°C respectively. Calculate the rate of heat flow through the window pane. Also find the temperatures of other interfaces. Given thermal conductivities of glass and air as 0.8 and 0.08 W m^_¹K^_1 respectively. [1997-5 marks]

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102.A sample of 2kg of mono-atomic helium (assumed ideal) is taken through the process ABC and another sample of 2kg of the same gas is taken through the process ADC (see figure). Given molecular mass of helium = 4

i)What is the temperature of helium in each of the states A,B,C and D?
ii)Is there any way of telling afterwards which sample of helium went through the process ABC and which went through the process ADC? Write yes or no.
iii)How much is the heat involved in each process ABC and ADC? [1997-5 marks]
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104.The apparatus shown in the figure consists of four glass columns a connected by horizontal sections. The height of two central columns B & C are 49 cm each. The two outer columns A & D are open to the atmosphere. A & C are maintained at a temperature of 95° C while the columns B & D are maintained at 5° C. The height of the liquid in A & D measured from the base are 52.8 cm & 51 cm respectively. Determine the coefficient of thermal expansion of the liquid. [1997-5 marks]

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105.One mole of an ideal mono- ‘ atomic gas is taken round 3P₀the cyclic process ABCA as shown in figure. Calculate

a)the work done by the gas
b)the heat rejected by the gas in the path CA and the heat absorbed by the gas in the path AB;
c)the net heat absorbed by the gas in the path BC;
d)the maximum temperature attained by the gas during the cycle. [1998-8 marks]
Ans.Number of mole of ideal monoatomic gas =n=l mole

106.A solid body X of heat capacity C is kept in an atmosphere whose temperature is T_A = 300 K. At time t = 0, the temperature of X is T₀ = 400K. It cools according to Newton’s law of cooling. At time t1 its temperature is found to be 350 K. At this time t1, the body X is connected to a larger box Y at atmospheric temperature T_A, through a conducting rod of length L, cross-sectional area A and thermal conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area A of the connecting rod is small compared to the surface area of X. Find the temperature of X at time t = 3t₁[1998-8 marks]
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107.Two moles of an ideal monatomic gas, initially at pressure P₍ and volume V_p undergoes an adiabatic compression until its volume is V₂. Then the gas is given heat Q at constant volume V₂.
a)Sketch the complete process on a P-V diagram
b)Find the total workdone by the gas, the total change in its internal energy and the final temperature of the gas. [Give your answer in terms P1,V1,V2, Q and R], [1999-10 marks]
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108.Two moles of an ideal mono- atomic gas taken through a cycle ABCA as shown in the P-T diagram. During the process AB, pressure and temperature of the gas vary such that PT = constant. If Tj = 300 K, calculate

a)the work done on the gas in the process AB and
b)the heat absorbed or released by the gas in each of the processes. Give answer in terms of the universal gas constant R. [2000-10 marks]
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109.An ice cube of mass 0.1 kg at 0°C is placed in an isolated container which is at 227°C. The specific heat S of the container varies with temperature T according to the empirical relation S = A + BT, where A = 100 cal/kg-K and B = 2 x 10^-2 cal/kg- K². If the final temperature of the container is 27°C, determine the mass of the container. (Latent heat of fusion of water = 8 x 10⁴ cal/kg. Specific heat of water = 10³ cal/kg-K) [2001-5 marks]
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110.A 5 m long cylindrical steel wire with radius 2 x l0^_3m is suspended vertically from a rigid support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses. (For the steel wire: Young’s modulus =2.1 x lO¹¹Pa; Density = 7860 kg/m³; Specific heat = 420 J / kg – K ). [2001-5 marks]
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112.A cubical box of side 1 meter contains helium gas (atomic weight 4) at a pressure of 100N/m². During an observation time of 1 second, an atom travelling with the root mean square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. Take R = (25/3)J/mol -K and k = 1.38 x l0-²³J/K [2002-5 marks]
a)Evaluate the temperature of the gas.
b)Evaluate the average kinetic energy per atom.
c)Evaluate the total mass of helium gas in the box.
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113.An insulated container containing mono atomic gas of molar mass M is moving with a velocity v₀. If the container is suddenly stopped, find the change in temperature.
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114.Hot oii is circulated through an insulated container with a wooden lid at the top whose conductivity K = 0.149 J/(m-°C-sec), thickness t = 5 mm, emissivity = 0.6. Temperature of the top of the lid is maintained at T_l = 127°. the ambient temperature T_a = 27°C. Calculate[2003-4 marks]

a)rate of heat loss per unit area due to radiation from the lid. .
b)temperature of the oil. (Given s = 17/3 x 10-⁸Wm-² K-⁴ )
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115.A diatomic gas is enclosed in a vessel fitted with mass less movable piston. Area of cross section of vessel is lm². Initial height of the piston lm (see the figure). The initial temperature of the gas is 300 K. The temperature of the gas is increased to 400K, keeping pressure constant. Calculate the new height of the piston. The piston is brought to its initial position with no heat exchange. Calculate the final temperature of the gas. You can leave answer in fraction. [2004-2 marks]
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116.A small spherical body of radius r is falling under gravity in viscous medium. Due to friction, the medium gets heated. How does the rate of heating depend on radius of body when it attains terminal velocity?
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119.A cylinder of mass 1kg is given heat of 20,000J at atmospheric pressure.If initially the temperature of cylinder is 20°C, find
a)final temperature of the cylinde
b)workdone by the cylinder
c)change in internal energy of the cylinder. (Given that specific heat of cylinder = 400J kg^-1 °CT^-1, co-efficient of volume expansion = 9 x lO^_^{5 0}CT^-1, Atmospheric pressure =10⁵N/m² and Density of cylinder = 9000 kg/m³)
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121.A piece of ice (heat capacity = 2100 J kg^-1 °C^_1and latent heat = 3.36 x lO⁵ J kg^-1) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of the heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
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122.A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. In the initial temperature of the gas is Ti₍ (in Kelvin) and the final temperature is a Ti, the value of a is
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123.Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T₁ and T₂, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?
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True /False Type
125.The root-mean square speeds of the molecules of different ideal gases, maintained at the same temperature are the same. [1981-2 marks]

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126.The volume V versus temperature T graphs for a certain amount of a’perfect gas at two pressure P1 and P₂ are as shown in figure. It follows from the graphs that P1 is greater than P₂. [1982-2 marks]

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127.Two different gases at the same temperature have equal root mean square velocities. [1982-2 marks]
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128.The curves A and B in the figure show P-V graphs for an isothermal and an adiabatic process for an ideal gas. The isothermal process is represented by the curve A. [1985-3 marks]

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129.At a given temperature, the specific heat of a gas at constant pressure is always greater than its specific heat at constant volume.
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130.The root mean square (rms) speed of oxygen molecules (0₂) at a certain temperature T (absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged. [1987-2 marks]
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131.Two spheres of the same material have radii lm and 4m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is greater than that by the second.[1988-2 marks]
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Fill in the blanks
132.One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is……………… [1984-2 marks]

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133.The variation of temperature of a material, as heat is given to it at a constant rate, is shown in the figure. The state of the material at the point P is…………. [1985-2 marks]

Ans.A to B represents a change which occurs at con¬stant temperature when heat is added to the sys¬tem.From O to A = Temperature increases at solid state. AB = It represents change of state from solid to liquid when heat is added.Since P lies on AB, the material is partly solid and partly liquid.

134.During an experiment, an ideal gas is found to obey an additional law VP² constant, The gas is initially at a temperature T, and volume V. When it expands to a volume 2V, the temperature becomes……………….[1987-2 marks]
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135. 300 grain of water at 25°C is added to 100 gram of ice at 0°C. The final temperature of the mixture is……… °C. [11989-2 marks]
Ans.Ice at o°Cgains heat first to melt int0 water at
0°Cand then this water gains heat for rise of its temperature if heat energy is available.
Heat required by ice for melting =mL

136.The earth receives, at its surface, radiation from the sun at the rate of 1400Win ² The dislance of the centre of tire sun from the surface of the earth is 1.5×10¹¹m and radius of the sun is 7×10⁸m. Treating the sun as a black body, it follows from the above data that its surface temperature is………K.[1989-2 marks]
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137.A solid copper sphere (density p and specific heats) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0 K. The time required for the temperature of the sphere to drop to 100 k is……….. [1991-2 marks]
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138.A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. If the temperature difference between the outer and inner surface of the shell is not to exceed T, the thickness of the shell should not be less than……. [1991-1 mark]
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139.A substance of mass M kg requires a power input of P watt to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t second. The latent heat of fusion of the substance is…………….[1992-1 mark]
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140.A container of volume 1 m³is divided into two equal parts by a partition. One part has an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be ……………………..[1993-1 mark]
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142.Two metal cubes A & B of same size are j tour arranged as shown in figure.The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A & B are 300 W/m° C and 200 W/m° C, respectively. After steady state is reached the temperature T of the interface will be ……………….[1996-2 marks]

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143.A ring shaped tube contains two ideal gases with equal masses and molar masses M, = 32 and M₂ = 28. The gases are separated by one fixed partition and another movable stopper S which can move freely without friction inside the ring. The angle a as shown in the figure is ………………… degree. [1997-2 marks]

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144.A gas thermometer is used as a standard thermometer for measurement of temperature, when the gas container of the thermometer is immersed in water at its triple point 273.16 K, the pressure in the gas thermometer reads 3.0 x l0⁴N/m². When the gas container of the same thermometer is immersed in another system, the gas pressure reads 3.5xl0⁴N/m² The temperature of this system is therefore ………………..°C [1997-1 mark]
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145.Earth receives 1400 W/m² of solar power . If all the solar energy falling on a lens of area 2 m² is focused on to a block of ice of mass 280 grams, the time taken to melt the ice will be……………..minute.(Latent heat of fusion of ice ~ 3.3 x 10⁵ J/kg) [1997-2 marks]
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JEE Main Home Maths Physics Chemistry

JEE Main Mathematics Complex Numbers Previous Year Papers Questions With Solutions

December 14, 2022

JEE Main Mathematics Complex Numbers Previous Year Papers Questions With Solutions

Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Mathematics Relations, Functions, and Reasoning Previous Year Papers Questions With Solutions

December 14, 2022

JEE Main Mathematics Relations, Functions, and Reasoning Previous Year Papers Questions With Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Relations and Functions Previous Year Questions with Solutions is given below.

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Ans.(3) Clearly/is both one – one and onto Because if n is odd, values are set of all non¬negative integers and if n is an even, values are set of all negative integers.

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Ans.(2) f(- x) = -f(x) an odd function

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Ans.(2) If y = y(x) is symmetric about the line x = 2 then f(2 + x) = f(2 – x).

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Ans.(1) Reflexive and transitive only.
e.g. (3, 3), (6, 6), (9, 9), (12, 12) [Reflexive] (3, 6), (6, 12), (3, 12) [Transitive]

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Ans.(3) There is no information about co-domain therefore f(x) is not necessarily onto.

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JEE Main Home Maths Physics Chemistry

JEE Main Physics Laws of Motion Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Laws of Motion Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Laws of Motion Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer
1.A ship of mass 3 x 10⁷ kg initially at rest is pulled by a force of 5 x 10⁴ N through a distance of 3m. Assuming that the resistance due to water is negligible, the speed of the ship is [1980-2 marks]
a) 1.5m/s b) 60 m/s
c) 0.1 m/s d) 5 m/s
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2.A block of mass 2kg rests on a rough inclined plane making an angle of 30° with the horizontal. The co-efficient of static friction between the block and the plane is 0.7. The frictional force on the block is [1980-2 marks]

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3.In the arrangement, shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed u. Pulleys A and B are fixed. Mass M moves upwards with a speed [1982-3 marks]

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4.During peddling of a bicycle, the force of friction exerted by the ground on the two wheels is such that it acts [1990-2 marks]
a)in the backward direction on the front wheel and in the forward direction on the rear wheel
b)in the forward direction on the front wheel and in the backward direction on the rear wheel
c)in the backward direction on both, the front and the rear wheels
d)in the forward direction on both, the front and the rear wheels.
Ans.(a) due to peddling, the point of contact of real wheel has a tendency to move backwards. So frictional force opposes the back ward tendency i,e., frictional force acts in the forward direction. But the back wheel accelerates the front wheel in the forward direction. To oppose this frictional force acts in the back ward direction on front wheel.

5.A car is moving in a circular horizontal track of radius 10m with a constant speed of lOm/s. A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the track is (g = 10 m/s²) [1992-2 marks]
a) zero b) 30° c) 45° d) 60°
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6.A block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is [1994-1 mark]
a) 2.5N b) 0.98N c) 4.9N d) 0.49N
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8.A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in [2001-2 marks]

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9.An insect crawls up a hemispherical surface very slowly (see fig.) The coefficient of friction between the insect and the surface is 1/3.If the line joining the center of the hemispherical surface to the insect makes an angle alpha with the vertical the maximum possible value of alpha is given by [2001-1 mark]

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a) 0° b) 30° c) 45° d) 60°
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11.A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by[2001-2 marks]

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12.What is the maximum value of the force F such that the block shown in the arrangement, does not move ? (g = 10ms^-2) [2003-2 marks]

a) 20N
b)10N
c)12N
d)15N
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13.A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k. The two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks? [2004-2 marks]

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14.A blook of mass m is at rest under the action of force F against a wall as shown in the figure. Which of the following statements is incorrect ?[2005-2 marks]

a)f = mg [where f is frictional force]
b)F = N [Where N is normal force]
c)F will not produce torque
d)N will not produce torque.
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15.Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string.The whole system is suspended by a massless spring as shown in the figure.The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively [2006-3 marks]

a) g, g/2 b) g/2, g c) g, g d) g/2, g/2
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16.Two particles of mass m each are tied at the., ends of a light string of length 2a. The whole system is kept on a frictionless ‘ a ‘ a horizontal surface with the string held tight so that each mass is at a distance a from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them [2007-3 marks]

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a) 0° b) 30° c) 45° d) 90°
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19.If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that [2009]
a)linear momentum of the system does not change in time
b)kinetic energy of the system does not change in time
c)angular momentum of the system does not change in time
d)potential energy of the system does not change in time
Ans.(a) Linear momentum remains constant if net external force on the system of parlicle is zero.

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21.A piece of wire is bent in the shape of a parabola y = kx² (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is [2009]

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Multiple Choice with ONE or More Than ONE correct answers
22.A reference frame attached to the earth [1986-2 marks]
a)is an inertial frame by definition.
b)cannot be an inertial frame because the earth is revolving round the sun.
c)is an inertial frame because Newton’s laws are applicable in this frame.
d)cannot be an inertial frame because the earth is rotating about its own axis.
Ans.(b), (d) a) It is incorrect. Earth is an accelerated frame, obviously it cannot be an inertial frame.
b)It is correct
c)It is incorrect
Newton’s laws are applicable to it only as a limiting case.
d)It is correct
Infact, a rotating or a revolving frame is accelerating and hence non-inertial. Options (b) and (d) are correct.

Assertion & Reasoning type
Instructions : Each question contains statement-1(Assertion) and statement – 2 (Reason). Of these
statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase
d)Statement-1 is false, statement-2 is true.
Ans.

23.Statement-1: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30°with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.
Statement-2 :The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination. [2007-3 marks]
Ans.(c) You need to be clever. Do not waste time on statement-1, statement-2, is false. And only in alternative (c), the statement -2 is false.

24.Statement-1 : A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
Statement-2 :For every action, there is an equal and opposite reaction. [2007-3 marks]
Ans.(b) The dishes will remain over there, their state of motion will not change, If the friction on them is not enough to change the state of motion as fast as that of the cloth.

25.Statement-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

Ans.(b) Statement-1 relates to visual experience. Statement -2 is also correct. It is just the method the relative velocity of an object w.r.t another is calculated. But it does not explains Statement-1. The correct explanation of Statement-1 is passed on the visual perception of motion, particularly the angular velocity. The object appears to be moving faster when its angular velocity is greater.

26.Statement-1 :It is easier to pull a heavy object than to push it on a level ground.
Statement-2 :The magnitude of frictional force depends on the nature of the two surfaces in contact.
Ans.(b) Statement-1 is practical experience of everyday life, it is true.Statement-2 is also true but is not the correct explanation of Statement -1. Correct explanation of statement-1 is “ there is an increase in the normal reaction when the object is pushed and there is a decrease in the normal reaction when object is pulled”.

Subjective / Numerical integer type
27.In the figure, the blocks A, B and C have masses 3kg, 4 kg and 8 kg respectively. The coefficient of sliding friction between any two surfaces is 0.25.A is held at rest by a massless rigid rod fixed to the wall, while B and C are connected by a light flexible cord passing around a fixed frictionless pulley. Find the force F necessary to drag C along the horizontal surface to the left at a constant speed. Assume that the arrangement shown in the figure, i.e, B on C and A on B, is maintained throughout.[1978]

Ans.When block C is moved to the left, the block B will move to right (due to reaction of C on B) while block A always remains at rest. Let T be the tension in the cord when blocks Band C move. The frictional forces between the different surfaces are as follows.

28.A uniform rope of length L and mass M is pulled by a constant force F. What is the tension in the rope at a distance l from the end where the force is applied? [1978]
Ans.

Ans.(a) Refer the figure. When the block moves down the inclined plane, the force of friciton f acts upwards along the plane. Let Fj be the force needed to make the block move without any acceleration. As the acceleration is zero, no net force acts on the block as its slides down the plane. Hence

30.Two blocks connected by a massless string slide do\frn an inclined plane having an angle of inclination of 37°. The masses of the two blocks are M! – 4kg and M₂ = 2kg respectively and the coefficients of friction of Mj and M₂ with the inclined plane are 0.75 and 0.25 respectively Assuming the string to be taut, find (i) the common acceleration of two masses and (ii) the tension in the string.
(sin 37° = 0.6, cos37° = 0.8) [Takeg = 9.8ms^-2]

Ans.

31.Masses M_p M₂ and M₃ are connected by strings of negligible mass which pass ^Mlover massless and frictionless pulleys Pj and P₂ as shown in the figure. The masses move such that the portion of the string between Pj and P₂ is parallel to the inclined plane and the portion of the string between P₂ and M₃ is horizontal. The masses M₂ and M₃ are 4.0kg each and the co-efficient of kinetic friction between the masses and the Surfaces is 0.25. The inclined plane makes an angle of 37° with the horizontal. If the mass Mj moves downwards with a uniform velocity, find
i)The mass of
ii)The tension in the horizontal portion of the string
(g = 9.8m/sec², sin37° =3/5) [1981-6 marks]

Ans.The question gives that mass Mj moves downwards with a uniform velocity. It means that net acceleration of the system is zero. It is possible if the net pulling force, due to weights of M,, M₂ & M₃ and frictional force, is zero.

32.A particle of mass m rests on a horizontal floor with which it has a co-efficient of static friction (X. It is desired to make the body move by applying the minimum possible force F. Find the magnitude of F and the direction in which it has to be applied. [1987-7 marks]
Ans.

33.Two blocks of mass 2.9 kg and 1.9 kg are suspended from a rigid support S by two inexten- sible wires each of length 1 meter, see figure. The upper wire has negligible mass and the lower wire has a uniform mass of 0.2kg/m.The whole system of blocks, wires and support have an upward acceleration of 0.2 m/s². Acceleration due to gravity is 9.8 m/s²[1989-6 marks]
i) Find the tension at the mid-point of the lower wire.
ii) Find the tension at the mid-point of the upper wire.

Ans.

Ans.

35.A smooth semic ircular wire- track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R/4 is attached to the lowest point O of the wire- track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle of 60° with the vertical. The spring constant K=mg/R. Consider the instant when the ring is released, and
i)draw the free body diagram of the ring,
ii)determine the tangential acceleration of the ring and the normal reaction.

Ans.

36.Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless inexten- sible string and a frictionless pulley as shown in the figure. The wedge is inclined at 45° to the horizontal on both sides. The coefficient of friction between block A and the wedge is 2/3 and that between block B and the wedge is 1/3. If the system of A and B is released from rest, find (i) The acceleration of A, (ii) Tension in the string, & (iii) The magnitude and the direction of the force of friction acting on A. [1997-5 marks]

Ans.

37.Two blocks of mass m1 = 10kg and m₂ = 5kg, connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of a turn table. The co-efficient of friction between the table and nijis 0.5 while there is no friction between rr^ and the table. The table is rotating with an angular velocity of lOrad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distance of 0.124m from O.The masses are observed to be at rest with respect to an observer on the turn table.[1997-5 marks]
a)Calculate the frictional force on m1
b)What should be the minimum angular speed of the turn table so that the masses will slip from this position?
c)How should the masses be placed with the string remaining taut, so that there is no frictional force acting on the mass m1?
Ans.

38.In the figure masses m1, m₂ and M are 20 kg, 5 kg and 50 kg respectively. The co-efficient of friction between M and ground is zero. The co-efficient of friction between m1 and M and that between m₂and ground is 0.3. The pulleys and the strings are massless. The string is perfectly horizontal between P, and m1 and also between P₂ and m₂ .The string is perfectly vertical between P, and P₂. An external horizontal force F is applied to the mass M. Take g = 10 m/s². [2000-10 marks]
(a)Draw a free-body diagram for mass M, clearly showing all the forces.
(b)Let the magnitude of the force of friction between m1 and M be f1 and that between m₂ and ground be f₂. For a p articular F it is found that f1 = 2 f₂ . Find f1 and f₂ .Write equations of motion of all the masses Find F, tension in the string and acceleration of the masses.

Ans.

Ans.

41.A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s², find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is relesed from rest.

Ans.

Ans.

True/ False Type
43.A rocket moves forward by pushing the surrounding air backwards. [1980]
Ans.False:A rocket is propelled not by pushing the surrounding air backwards but by the ejection of a portion of its mass to the back. The forward force on the rocket is the reaction to the backward force on the ejected material and as more material is ejected, the mass of the rocket decreases.

44. When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the direction of his motion.[1981-2 mark]
Ans.False:When a person walks on a rough surface, he pushes the foot backward . The motion of the surface of contact is backward. Therefore the frictional force will act in the forward direction which is the direction of motion of the person, the statement is false.

45.The pulley arrangements of figure (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force F = 2mg. The acceleration of m is the same in both cases. [1984-2 marks]

Ans.

Fill in the blanks
46.A block of mass 1kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6. If the acceleration of the truck is 5 m/s², the frictional force acting on the block is newton.[1984-2 marks]
Ans.

Ans.

JEE Main Home Maths Physics Chemistry

JEE Main Physics Semiconductor Devices Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Semiconductor Devices Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Semiconductor Devices Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer

Ans.

2.The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature [1995]
a) increases exponentially with increasing band gap
b) decreases exponentially with increasing ban gap
c) decreases with increasing temperature
d) is independent of the temperature and the band gap
Ans.

3.A full wave rectifier circuit along with the output is shown in figure. The contribution(s) from the diode 1 is (are) [1996-2 marks]

Ans.(c)As given in the figure, diode (1) is reverse biased in first half cycle and hence nonconducting.

During the second half cycle, diobe (1) is forward biased and hence conducting.Thus diode (1) conducts only in a alternate half cycles. The contributions from the diode (1) are B and D.

4.The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The badn gap (in eV) for the semiconductor is[1997-1 mark]
a) 0.9 b) 0.7 c) 0.5 d) 1.1
Ans.

5.The dominant mechanisms for motion of charge carriers in forward and reverse biased silicon p-n junctions are [1997-1 mark]
a) drift in forward bias, diffusion in reverse bias
b) diffusion in forward bias, drift in reverse bias
c) diffusion in both forward and reverse bias
d) drift in both forward and reverse bias.
Ans.(b) Drift current flows form p— side to n — side.Diffusion current flows from n — side to p – side. In forward biasing, drift current is greater than the diffusion current.In reverse biasing, the diffusion current is greater than the drift current.Option (b) represents the answer.

6.The circuit shown in the figure contains two diodes each with a forward resistance of 50 ohm and with infinite backward resistance. If the battery voltage is 6 V, the current through the 100 ohm resistance (in ampere)is [1997-1 mark]
a) zero b) 0.02 c) 0.03 d) 0.036

Ans.

7.Which of the following statements is not true?
a) The resistance of intrinsic semiconductor decreases with increase of temperature
b) Doping pure Si with trivalent impurties gives p -type semiconductors
c) The majority carriers in n-type semiconductors are holes
d) A p-n junction can act as a semiconductor diode.[1997-1 mark]
Ans.(c) Statement (c) is not true.The majority carriers in n— type semiconductors are electrons, not holes.

Multiple Choice with ONE or More Than ONE correct answers

8.Select the correct statement from the following: [1984 – 2 Marks]
a) A diode can be used as a rectifier
b) A triode cannot be used as a rectifier
c) The current in a diode is always proportional to the applied voltage
d) The linear portion of the I- V characteristic of a triode is used for amplification without distortion.
Ans.(a)A diode can be used as a rectifier. Option (a) is correct Other options are not correct.

9.For a given plate voltage, the plate current in a triode value is maximum when the potential of
[1985-2 marks]
a) the grid is positive and plate is negative
b) the grid is zero and plate is positive
c) the grid is negative and plate is positive
d) the grid is positive and plate is positive.IIT
Ans.For maximum plate current in a triode value is available, for a given plate voltage, when grid is positive and plate is positive.

10.The impurity atoms, with which pure silicon should be doped to make a p -type semiconductor, are those of [1988-2 marks]
a) phosphorus b) boron
c) antimony d) aluminium.
Ans.(b), (d) p — type semiconductor is obtained when Si or Ge (tetravalent) is doped with group III trivalent impurities like aluminium, boron etc.

11.Two identical p — n junctions may be connected in series with a battery in three ways, as shown in figure. The potential drops across the two p — n junctions are equal in [1989-2 makrs]

a)circuit 1 and circuit 2
b) circuit 2 and circuit 3
c) circuit 3 and circuit 1
d) circuit 1 only
Ans.The potential drops across the two p — ti junctions, connected in series, are equal in circuit 2 and circuit 3. These two circuits are either forward biased or reverse biased in terms of the p — n junctions.

12.In an n — p — n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector, [1992-2 marks]
a) the emitter current will be 9 mA
b) the base current will be 1 mA
c) the emitter current will be 11 mA
d) the base current will be -1 mA.
Ans.

13.Holes are charge carrier in [1996-2 marks]
a) intrinsic semiconductors b) ionic solids
c) p — type semiconductors d) metals
Ans.(a), (c) In intrinsic semiconductor, n_h — n_eIn p — type semiconductor , n_h > n_e

14.A transistor is used in the common emitter mode as an amplifier. Then [1998-2 marks]
a) the base-emitter junction is forward-biased.
b) the base-emitter junction is reverse-biased.
c) the input signal is connected in series with the voltage applied to bias the base-emitter junction.
d) the input signal is connected in series with the voltage applied to bias the base-collector junction.
Ans.(a), (c) When a transistor is used in the common emitter mode as an amplifier, then the options (a) and (c) are correct.

15.In a p — n junction diode, not connected to any circuit, [1998-2 marks]
a) the potential is the same every where
b) the stype side is at a higher potential than the n — type side.
c) there is an electric field at the junction directed from the n — type side to the p — type side.
d) there is an electric field at the junction directed fromt he p — type side to the n — type side.
Ans.(c) In a p — n junction diode, a depletion layer or a potenial barrier is formed. The n— side of depletion layer is at higher potential; and p — side is at lower potential.

Subjective / Numerical integer type
16.A triode has plate characteristics in the form of parallel lines in the region of our interest. At a grid voltage of -1 volt the anode current / (in milli ampere) is given in terms of plate voltage V(in volt) by the algebraic relation:
I = 0.125V-7.5 .
For grid voltage of -3 volt, the current at anode voltage of 300 volt is 5 milliampere. Determine the plate resistance (rp), transconductance (gm) and the amplification factor ( )for the triode.[1987-7 marks]
Ans.

True / False Type
17.For a diode the variation of its anode current Ia with the anode voltage Va at two different cathode temperatures T1 and T2 is shown in the figure. The temperature T2 is greater than T1. [1986- 3 marks]

Ans.TRUE : With increase in cathode temperature, the number of electrons emitted from cathode increases. Consequently the anode current increases

Fill in the blanks
18.In the forward bias arrangement of a p-n junction rectifier, the p end is connected to the……. terminal
of the battery and the direction of the current is from……. to……… in the rectifier. [1988-2 marks]
Ans.The p -end is connected to positive terminal. Direction of current is from p to

19…………..biasing of p-n junction offers high resistance to current flow across the junction. The biasing is obtained by connecting the p- side to the……… terminal of the battery. [1990-2 marks]
Ans.Reverse biasing is obtained when p— side is connected to the negative terminal of battery.

20.For the given circuit shown in fig. to act as full wave rectifier, the a.c. input should be connected across …………….and……….. and the d.c. output would appear across…………. and…………….. [1991-1 mark]

Ans.B and D: for a.c.input
A and C: for d.c. output

21.In a………….. biased p-n junction, the net flow of holes is from the n region to the p region.[1993 -1 mark]
Ans.The given property is related with reverse biased p — n

JEE Main Home Maths Physics Chemistry

JEE Main Physics Units, Dimensions and Errors Previous Year Questions with Solutions

December 14, 2022

JEE Main Physics Units, Dimensions and Errors Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation, JEE Main Physics Units, Dimensions and Errors Previous Year Questions with Solutions is given below.

Multiple Choice with ONE correct answer

1.In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in MKSQ system ? [1995-2 marks]

Ans.

Ans.

(a)resistance (b) charge
(c) voltage ( d) current
Ans.

Ans.

6.A wire of length 1 = 6±0.06cm and radius r = 0.5 ± 0.005cm and mass m = 0.3 ± 0.003g . Maximum percentage error in density is [2004-2 marks]
(a) 4 (b) 2 ( c) 1 ( d) 6.8
Ans.

7.Which of the following sets have different dimensions ? [2005-2 marks]
(a)Pressure, Young’s modulus, stress
(b)Emf, potential difference, electric potential
(c)Heat, work done, energy
(d)Dipole moment, electric flux, electric field
Ans.

8.The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentange error in the density is
(a) 0.9% (b) 2.4% (c) 3.1% (d) 4.2%
Ans.
<

Multiple Choice with ONE or More Than ONE correct answers

9.If L,C,R represent inductance, capacitance and resistance respectively, the combinations having dimensions of frequency are [1984-2 marks]

Ans.

10.Which of the following combinations have the dimensions of time ? L,C,R represent inductance, capacitance and resistance respectively [1986-2 marks]

Ans.

11.The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair(s) [1986-2 marks]
(a) Torque and work (b) Angular momentum and work
(c) Energy and Young’s modulus (d) Light year and wavelength
Ans.

12.The dimensions of length are expressed as G^xc^yh^z .where G,c and h are the universal gravitational constant, speed of light and Planck’s constant respectively, then [1992-2 marks]

Ans.

13.The pairs of physical quantities that have the same dimensions in (are) [1995-2 marks]
(a)Reynolds number and coefficient of friction
(b)Curie and frequency of a light wave
(c)Latent heat and gravitational potential
(d)Planck’s constant and torque
Ans.

Ans.

15.The ST unit of inductance, the henry can be written as [1998-2 marks]
(a)weber/ampere (b) volt-sec/amp
(c) joule/(ampere)² (d) ohm-second
Ans.

Matching Type

16.Match the physical quantities given in Column 1 with dimensions expressed in terms of mass (M), length (L), time (T), and charge (Q) given in Column II

Ans.

17.Column-I gives three physical quantities. Select the appropriate units for the choices given in Column-II. Some of the physical quantities may have more than one choice correct [1990-3 marks]

Ans.

18.Some physical quantities are given in column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in column I with the units in Column II. [2007-6 marks]

Ans.

Subjective / Numerical integer type

19.Give the MKS units for each of the following quantities : [1980-3 marks]
i) Young’s modulus ii) Magnetic induction iii) Power of a lens
Ans.

20.A gas bubble, from an explosion under water, oscillates with a period T proportional to p^ad^bE^c • Where P is the static pressure, d is the density of water and E is the total energy of the explosion. Find the values of a,b and c [1981-3 marks]
Ans.

21.Write the dimensions of the following in terms of mass, time, length and charge
i) magnetic flux ii) rigidity modulus [1982-2 marks]]
Ans.

Fill in the blanks

22.Planck’s constant has dimensions…………… [1985-2 marks]
Ans.

23.In the formula X = 3YZ²,X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are………………………………. [1988-2 marks]
Ans.