JEE-Physics 3. A particle of mass 1kg has velocity (2t)ˆi and another particle of mass 2 kg has velocity (t2 ) ˆj . 4. v1 v2 5. Column I Column II E (A) Net force on centre of mass at 2 s (p) 20 9 unit (B) Velocity of centre of mass at 2s (q) 68 unit (C) Displacement of centre of mass in 2s (r) 80 (s) unit 3 None Two blocks A and B of mass 2m and m respectively are connected by a massless spring of spring constant k. This system lies over a smooth horizontal surface. At t = 0 the block A has velocity u towards right as shown while the speed of block B is zero, and the length of spring is equal to its natural length at that instant. In each situation of column–I, certain statements are given and corresponding results are given in column II. B kA m 2m u smooth horizontal surface Column I Column II (A) The velocity of block A (p) Can never be zero (B) The velocity of block B (q) May be zero at certain instants of time (C) The kinetic energy of system of two blocks (r) is minimum at maximum (D) The potential energy of spring compression of spring (s) Is maximum at maximum extension of spring In each situation of column–I, a system involving two bodies is given. All strings and pulleys are light and friction is absent everywhere. Initially each body of every system is at rest. Consider the system in all situation of column I from rest till any collision occurs. Then match the statements in column – I with the corresponding results in column–II Column I Column II (A) The block plus wedge system is placed over m (p) Shifts towards right smooth horizontal surface. After the system M is released from rest, the centre of mass of system (B) The string connecting both the blocks m (q) Shifts downwards of mass m is horizontal. Left block is m NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 placed over smooth horizontal table as shown. After the two block system is released from rest, the centre of mass of system (C) The block and monkey have same mass. The (r) Shifts upwards monkey starts climbing up the rope. After the monkey starts climbing up, the centre of mass of monkey + block system (s) Does not shift (D) Both block of mass m are initially at rest. The mm left block is given initial velocity u downwards. Then, the centre of mass of two block system afterwards 63
JEE-Physics 6 . If net force on a system of particles is zero, then (p) Column II (q) Constant Column I (r) Zero (A) Acceleration of centre of mass (s) (B) Velocity of centre of mass May be zero (C) Momentum of centre of mass May be constant (D) Velocity of an individual particle of the system 7. Column I Column II (A) Elastic collision (p) KE is conserved (B) Inelastic collision (q) KE after collision = KE before collision (C) Perfectly inelastic collision (r) KE after collision KE before collision (s) Particles stick after collision (t) Linear momentum is conserved (u) Relative velocity of separation after is zero ASSERTION & REASON TYPE QUESTIONS These questions contains, Statement 1 (assertion) and Statement 2 (reason). 1 . S t a t e m e n t – 1 : In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun. and S t a t e m e n t – 2 : In firing, momentum is conserved. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 . S t a t e m e n t – 1 : When a girl jumps from a boat, the boat slightly moves away from the shore. and S t a t e m e n t – 2 : The total linear momentum of an isolated system remain conserved. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 3 . S t a t e m e n t – 1 : In a two body collision, the momenta of the particles are equal and opposite to one another, NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 before as well as after the collision when measured in the center of mass frame. and S t a t e m e n t – 2 : The momentum of the system is zero from the centre of mass frame. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 4 . S t a t e m e n t – 1 : The centre of mass and centre of gravity of a body are two different positions in general. and S t a t e m e n t – 2 : The centre of mass and centre of gravity of a body coincide if gravitational field is uniform. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 64 E
JEE-Physics 5 . S t a t e m e n t – 1 : A particle of mass m strikes a smooth wedge of mass M m v0 as shown in the figure. Linear momentum of particle along the inclined surface of wedge is conserved during collision. M and S t a t e m e n t – 2 : Wedge exerts a force on particle perpendicular to inclined Smooth face of wedge during collision. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 6 . S t a t e m e n t – 1 : The coefficient of restitution is less than one for all collisions studied under Newton’s laws of restitution. and S t a t e m e n t – 2 : For a perfectly elastic collision, coefficient of restitution is equal to one. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 7 . S tatem ent–1 : No external force acts on system of two spheres which undergo a perfectly elastic head on collision. The minimum kinetic energy of this system is zero if the net momentum of this system is zero. and S tatem ent–2 : In any two body system undergoing perfectly elastic head on collision, at the instant of maximum deformation, the complete kinetic energy of the system is converted to deformation potential energy of the system. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 8 . S t a t em e n t – 1 : A sphere of mass m moving with speed u undergoes a perfectly elastic head on collision with another sphere of heavier mass M at rest (M>>>m), then direction of velocity of sphere of mass m is reversed due to collision [no external force acts on system of two spheres] and S t a t em e n t – 2 : During a collision of spheres of unequal masses, the heavier exerts more force on lighter mass in comparison to the force which lighter mass exerts on heavier mass. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 9 . S tatem ent–1 : If a ball projected up obliquely from the ground breaks up into several fragments in its path, the centre of mass of the system of all fragments move in same parabolic path compared to initial one till all fragments are in air. and S t a t em e n t – 2 : In the situation of statement–1, at the instant of breaking, the fragments may be thrown in different directions with different speeds. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. E 65
JEE-Physics COMPREHENSION BASED QUESTIONS Comprehension # 1 If net force on a system in a particular direction is zero (say in horizontal direction) we can apply: m x R = m x , m v R = m v and m a R = m a L R L L R LL R L Here R stands for the masses which are moving towards right and L for the masses towards left, x is displacement, v is velocity and a the acceleration (all with respect to ground). A small block of mass m = 1 kg is placed over a wedge of mass M = 4 kg as shown in figure. Mass m is released from rest. All surfaces are smooth. Origin O is as shown. m 4m M 2m O 4m +x-axis 1 . Final velocity of the wedge is ..................... m/s :– (A) 3 (B) 2 1 1 (C) 2 (D) 3 (D) 6.8 2 . The block will strike the x–axis at x = ................m :– (A) 4.2 (B) 7.6 (C) 5.6 3 . Normal reaction between the two blocks at an instant when absolute acceleration of m is 5 3 m/s2 at 60° with horizontal is ........... N. Normal reaction at this instant is making 30° with horizontal : (A) 6 (B) 1 0 (C) 4 (D) 5 4 . At the same instant reaction on the wedge from the ground is .............. N. (A) 42.5 (B) 4 0 (C) 43.46 (D) None of these Comprehension # 2 When two bodies collide normally they exert equal and opposite impulses on each other. Impulse = change in linear momentum. Coefficient of restitution between two bodies is given by :– e |Re lative velocity of separation| = 1, for elastic collision velocity of approach| |Re lative 2kg 4m/s NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 1kg 6m/s Two bodies collide as shown in figure. During collision they exert impulse of magnitude J on each other. 1 . If the collision is elastic, the value of J is ................... N–s : (A) 10/3 (B) 5/4 (C) 8/3 (D) 3/2 2 . For what values of J (in N–s) the 2 kg block will change its direction of velocity : (A) J < 12 (B) J > 12 (C) J < 10 (D) J > 10 66 E
JEE-Physics Comprehension # 3 In an oblique collision component parallel to common tangent remains unchanged while along common normal direction, relative velocity of separation becomes e times the relative velocity of approach. 1 . A ball collides at B with velocity 10 m/s at 30° with vertical. There is a flag at A and a wall at C. Collision of ball with ground is perfectly inelastic (e = 0) and that with wall is elastic (e = 1). Given AB = BC = 10m. The ball will collide with the flag after time t = ......s. 30° (A) 4 A BC (C) 6 (B) 5 (D) Ball will not collide with the flag Comprehension # 4 When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by : dm F vr dt Here vr is the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/s.Total mass of gas is 20 kg. Coefficient of friction between the car and road is µ = 0.1. 1 . Car will start moving after time t = ............... second : (A) 4 (B) 1 0 (C) 5 (D) 8 2 . Maximum speed of car will be v = ................. m/s : (Take n 4 = 0.28) (D) 1.2 3 (D) 5.8 (A) 0.6 (B) 0.8 (C) 1.0 3 . Car will stop after (from starting) t = ............. seconds : (A) 12.2 (B) 6.4 (C) 10.6 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 Comprehension #5 One particle of mass 1 kg is moving along positive x–axis with velocity 3 m/s. Another particle of mass 2 kg is moving along y–axis with 6 m/s. At time t = 0, 1 kg mass is at (3m, 0) and 2 kg at (0, 9m), x–y plane is the horizontal plane. (Surface is smooth for question 1 and rough for question 2 and 3) 1 . The centre of mass of the two particles is moving in a straight line which equation is : (A) y = x + 2 (B) y = 4x + 2 (C) y = 2x – 4 (D) y = 2x + 4 2 . If both the particles have the same value of coefficient of friction = 0.2. The centre of mass will stop at time t = ......s : (A) 1.5 (B) 4.5 (C) 3.0 (D) 2.0 3 . Co–ordinates of centre of mass where it will stop finally are :– (A) (2.0 m, 14.25 m) (B) (2.25 m, 10 m) (C) (3.75 m, 9 m) (D) (1.75 m, 12 m) E 67
JEE-Physics Comprehension # 6 A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure. rough 15 m/s 1kg 2kg smooth 1 . The correct graph showing linear momentum of 1 kg (i.e. p1) and of 2kg (i.e. p2) versus time is : p1 and p2 p2 p1 and p2 p1 and p2 p1 and p2 p2 p1 p1 (A) (B) p1 p1 and p2 P1 (D) t p2 (C) t P2 t t 2 . If coefficient of friction between the two blocks is equal to 0.4, then magnitude of initial slope of p versus 1 t and p versus t (in SI unit) will be :– 2 (A) 4 and 2 (B) 2 and 4 (C) 4 and 4 (D) 2 and 2 3 . Momentum of both the blocks are equal at time t = ..............seconds : (A) 1.75 (B) 1.875 (C) 2.5 (D) 1.25 Comprehension # 7 k mF Two blocks of equal mass m are connected by an unstretched spring and the system m is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. 1 . Then the displacement of the centre of mass at time t is :- Ft2 Ft2 Ft2 Ft2 (A) (B) (C) (D) 2m 3m 4m m 2 . If the extension of the spring is x0 at time t, then the displacement of the first block at this instant is :- 1 Ft2 1 Ft2 1 Ft2 Ft2 (A) 2 2m x0 2m x0 (C) 2 2m x0 (D) 2m x0 (B) 2 3 . If the extension of the spring is x0 at time t, then the displacement of the second block at this instant is :- (A) Ft2 x0 (B) 1 Ft2 x0 (C) 1 2Ft2 x0 (D) 1 Ft2 x0 2m 2 2m 2 m 2 2m Comprehension # 8 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass mA and piece B with mass mB. Two pieces then move across the floor along x–axis. Graph of position versus time for the two pieces are given. x B xA x x xx A A t A t t A 2 t t t B (I) A B B (VI) B B (IV) (V) (II) (III) 68 E
JEE-Physics 1 . Which graphs pertain to physically possible explosions ? (A) II, V (B) VI (C) I, III (D) IV 2 . Based on the above question, Match column A with the column B. Column A Column B (Graph number) (P) mA = mB (Q) mA > mB I (R) mA < mB II III IV V VI (A) P – VI, Q – III, R – I (B) P – II, Q – V, R – IV (C) P – II, Q – IV, R – V (D) P – VI, Q – II, R – IV 3 . If all the graphs are possible then, in which of the following cases external force must be acting on the box :- (A) II (B) V (C) VI (D) I MISCELLANEOUS TYPE QUESTION ANSWER KEY EXERCISE –3 True / False 1. F 2. F 3. F 3mv2 2. 5 × 10–3 3. (0.8)6h 4. 25 5. External force F i l l i n t h e B l ank s 1. 2 6. Linear momentum mv 7. m Ax 8. 120 Ma t c h t h e C o l u m n 1. A–r, B–t, C–t, D–s 2. A–q, B–p, C–s 3. A–q, B–r, C–p 4. A–p,r, B–q,r, C–p,r, D–q,s NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 5. A–q, B–p, q, C–r, D–s 6. A–q, B–p,r, C–p,r, D–r,s 7. A–q,t, B–r,t, C–r,s,t,u Assertion – Reason 1. A 2. A 3. A 4. B 5.A 6.B 7. C 8. C 9. B Comprehension Based Questions Comprehension #1 : 1. B 2.D 3. D 4. A 2. B Comprehension #2 : 1. C 3. C 2. A 3. D Comprehension #3: 1. C 2. C 3. C 2. C 3. D Comprehension #4 : 1. C 2. A 3. C,D 2. B Comprehension #5 : 1. B Comprehension #6 : 1. D Comprehension #7 : 1. C Comprehension #8 : 1. A,D E 69
JEE-Physics EXERCISE–04 [A] CONCEPTUAL SUBJECTIVE EXERCISE 1 . Figure shows a uniform square plate from which four identical squares at the corners will be removed. (i) Where is the centre of mass of the plate originally. (ii) Where is C.M. after square 1 is removed. (iii) Where is C.M. after squares 1 and 2 removed. (iv) Where is C.M. after squares 1 and 3 are removed. (v) Where is C.M. after squares 1, 2 and 3 are removed. (vi) Where is C.M. after all the four squares are removed. Give Answers in terms of quadrants and axes. 2 . Four particles of masses m, 2m, 3m, 4m are placed at corners of a square of side 'a' as shown in fig. Find out coordinates of centre of mass. 3 . A rigid body consists of a 3 kg mass connected to a 2 kg mass by a massless rod. The 3kg mass is located at r1 (2i 5j) m and the 2 kg mass at r2 (4i 2j) m. Find the length of rod and the coordinates of the centre of mass. 4 . Three rods of the same mass are placed as shown in the figure. Calculate the coordinates of the centre of mass of the system. 5 . A man has constructed a toy as shown in fig. If density of the material of the sphere is 12 times of the cone compute the position of the centre of mass. [Centre of mass h of a cone of height h is at height of from its base.] 4 mA Determine the centre of gravity of a thin homogeneous 6. r C plate having the form of a rectangle with sides r and 2r O r NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 from which a semicircle with a radius r is cut out of figure. B 7 . A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate as shown in figure. Find the position of the centre of mass of the remaining portion. 42 cm 56 cm 8 . The figure shows a square metal plate of side from which a square plate of side y a has been cut as shown in the figure. Find the ratio (a/) so that the centre of mass A a of the remaining L–shaped plate coincides with the point A . o x a 70 E
JEE-Physics 9 . A thin sheet of metal of uniform thickness is cut into the shape bounded by the y x line x=a and y = ± kx2, as shown. Find the coordinates of the centre of mass. y=kx2 1 0 . In the figure shown, when the persons A and B exchange their positions, then y=-kx2 (i) the distance moved by the centre of mass of the system is _____. A B (ii) the plank moves toward _______. (iii) the distance moved by the plank is ____. m1 M m2 (iv) the distance moved by A with respect to ground is _____. 2m (v) the distance moved by B with respect to ground is __. m1= 50kg; m2= 70kg;M = 80kg 11 2 bodies m & m of mass 1 and 2 kg respectively are moving along x–axis under x(in m) 12 the influence of mutual force only. The velocity of their centre of mass at a given 1 instant is 2 m/s. The x–coordinate of m is plotted against time. Then plot the 1 x–coordinate of m against time (Both are located at origin). 1 2 t(in m) 2 12 . A body of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1 : 1 : 3. The two pieces of equal mass fly–off perpendicular to each other with a speed of 30 m/s each. What is the velocity of the heavier fragment ? 1 3 . Two bodies of same mass tied with an inelastic string of length lie together. One of them is projected vertically upwards with velocity 6g . Find the maximum height up to which the centre of mass of system of the two masses rises. 1 4 . A man whose mass is m kg jumps vertically into air from a sitting position in which his centre of mass is at a height h from the ground. When his feet are just about to leave the ground his centre of mass is h from 12 the ground and finally rises to h when he is at the top of the jump. What is the average upward force exerted 3 by the ground on him? 1 5 . A uniform thin rod of mass M and length L is standing vertically along the y–axis on a smooth horizontal surface, with its lower end at the origin (0, 0). A slight disturbance at t = 0 causes the lower end to slip on the smooth surface the positive x–axis, and the rod starts falling. (i) What is the path followed by the centre of mass of the rod during its fall ? (ii) Find the equation of the trajectory of a point on the rod located at a distance r from the lower end. What is the shape of the path of this point ? m 1 6 . A hemisphere of radius R and of mass 4m is free to slide with its base on NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 a smooth horizontal table. A particle of mass m is placed on the top of the 4m R hemisphere. Find the angular velocity of the particle relative to hemisphere an angular displacement when velocity of hemisphere has become v. 1 7 . A ball of mass 100 g is projected vertically upwards from the ground with a velocity of 49m/s. At the same time another identical ball is dropped from a height of 98 m to fall freely along the same path as that followed by the first ball. After some time the two balls collide and stick together and finally fall to the ground. Find the time of flight of the masses. 18. A block of mass M with a semicircular track of radius R, rests on a mR horizontal frictionless surface. A uniform cylinder of radius r and mass E m is released from rest at the top point A (see Fig). The cylinder slips M on the semicircular frictionless track. How far has the block moved when B the cylinder reaches the bottom (point B) of the track ? How fast is the block moving when the cylinder reaches the bottom of the track ? 71
JEE-Physics 1 9 . Two bodies A and B of masses m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity v along the line joining A and B and collides 0 elastically with A as shown in fig. At a certain instant of time t0 after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be x . 0 Determine – (i) the common velocity of A and B at time t and CA B 0 (ii) the spring constant. 2 0 . A sphere of mass m1 in motion hits directly another sphere of mass m2 at rest and sticks to it, the total kinetic energy after collision is 2/3 of their total K.E. before collision. Find the ratio of m : m . 12 L 2 1 . A simple pendulum is suspended from a peg on a vertical wall. The pendulum is pulled away from the wall to a horizontal position (see fig.) and released. The ball hits the wall, the coefficient of restitution being 2 Y 5 . What is the minimum number of collisions after which the amplitude 6R M,R of oscillations becomes less than 60 degrees ? O X 2 2 . A small sphere of radius R is held against the inner surface of a larger 4M(L,0) sphere of radius 6R. The masses of large and small spheres are 4M and M respectively. This arrangement is placed on a horizontal table. There is no friction between any surfaces of contact. The small sphere is now released. Find the co–ordinates of the centre of the larger sphere when the smaller sphere reaches the other extreme position. 2 3 . The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown in figure. How high does the bob A rise after the collision? Neglect the size of the bob and assume the collision to be elastic. 0.1kg 2 4 . A massless platform is kept on a light elastic spring, shown in Fig. When a sand particle of 0.1 kg mass is dropped on the pan from a height 0.24 m, the particle strikes the pan, and the spring compresses by 0.01 m. From what height should the particle be dropped to cause NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 a compression of 0.04 m ? 2 5 . In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)? 2 6 . A body 'A' moving in a straight line with velocity v makes a collision with a body 'B' initially at rest. After collision, B acquires a velocity of 1.6 v. Assuming the bodies to be perfectly elastic, what is the ratio of the mass of A to that of B? What percentage of A's energy is transferred to B as a result of collision. 2 7 . A particle of mass 2 kg moving with a velocity 5 i m/s collides head–on with another particle of mass 3 kg moving with a velocity 2i m/s. After the collision the first particle has speed of 1.6 m/s in negative x direction. Find : (i) Velocity of the centre of mass after the collision (ii) Velocity of the second particle after the collision (iii) Coefficient of restitution. E 72
2 8 . Three particles A, B and C of equal mass move with equal speed v JEE-Physics along the medians of an equilateral triangle as shown in fig. They collide at the centroid G of the triangle. After the collision, A comes to rest, A B retraces its path with the speed v. What is the velocity of C ? G BC 2 9 . Block A of mass m/2 is connected to one end of light rope which m/2 A g/6 passes over a pulley as shown in the Fig. Man of mass m climbs the other m end of rope with a relative acceleration of g/6 with respect to rope find acceleration of block A and tension in the rope. 3 0 . Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on 1m smooth table & B is held at the position shown. Mass B is now gently lifted 2m B up to the pulley and allowed to fall from rest. Determine up to what height A will A rise for the ensuing motion. 3 1 . Three identical balls each of mass m = 0.5 kg are connected with each other as shown in Fig. and rest over a smooth horizontal table. At moment t = 0, ball B is imparted a horizontal velocity v =9ms–1. Calculate 0 velocity of A just before it collides with ball C. v0 AB C CONCEPTUAL SUBJECTIVE EXERCISE ANSWER KEY EXERCISE–4(A) 1. (i) at O, (ii) diagonally from O to 3 (iii) along OY', (iv) at O (v) diagonally from O to 4 (vi) at O 2. a , 7a 2 10 3. 13 m, 14 , 19 4. a , a 2r 5 5 3 3 5. 4R from O 6. OC = 3 4 7. 9 cm from centre of NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 bigger circle (leftwards) 5 1 3a 11. 6m 8. 2 9. x= 10. (i) zero (ii) right (iii) 0.2 m (iv) 2.2 m (v) 1.8 m 4 mg h3 h1 (i) straight line h2 h1 12. 10 2 ms–1 at 450 13. 14. 15. x2 y2 , 2.5m (ii) =1 2 + r2 m R r 2gR r L r 12 M M m R 5v 17. 6.53 s 18. Mm , m 16. R cos v0 (ii) 2 m v 2 3 0 19. (i) 20. 2:1 21. 4 22. (L+2R, 0) 23. bob A does not rise 24. 3.96 m 25. No 3 x 2 0 4 4g 13mg 26. 64% 27. (i) 0.8ˆi ms–1 (ii) 2.4ˆi ms–1(c) 7 28. vC vB 29. , 30. 1.25 m 31. 6 ms–1 9 18 E 73
JEE-Physics EXERCISE–04 [B] BRAIN STORMING SUBJECTIVE EXERCISE 1 . A bullet of mass M is fired with a velocity 50 m/s at an angle with the horizontal. At the highest point 10 of its trajectory, it collides head–on with a bob of mass 3M suspended by a massless string of length 3 metres and gets embedded in the bob, after the collision the string moves through an angle of 120°. Find : (i) the angle , (ii)the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. (Take g = 10 m/s2). 2 . An object of mass 5 kg is projected with a velocity of 20 m/s at an angle of 60° to the horizontal. At the highest point of its path the projectile explodes and breaks up into two fragments of masses 1 kg and 4 kg. The fragments separate horizontally after the explosion. The explosion releases internal energy such that the kinetic energy of the system at the highest point is doubled. Calculate the separation between the two fragments when they reach the ground. A 3 . Two blocks of masses m and m are connected by a massless pulley A, m2 12 m1 slides along the smooth sides of a rectangular wedge of mass m, which rests on a smooth horizontal plane. Find the distance covered by the wedge on hm the horizontal plane till the mass m is lowered by the vertical distance h. 1 4 . The 4 kg sphere from rest when =60° strikes a block mass of 5 kg placed on a rough horizontal plane and comes to rest after collision. The 5 kg block 1m comes to rest after moving a distance of 0.8m. Find µ of ground & block & 4kg coefficient of restitution e. 5kg 5 . Two particles A and B of mass 2m and m respectively are attached to the ends of a light inextensible string of length 4a which passes over a small smooth peg at a height 3a from an inelastic table. The system is released from rest with each particle at a height a from the table. Find– (i) The speed of B when A strikes the table. (ii) The time that elapses before A first hits the table. (iii) The time for which A is resting on the table after the first collision & before it is first jerked off. 6 . Two particles, each of mass m, are connected by a light inextensible string of length 2. Initially they lie on a smooth horizontal table at points A and B distant apart. The particle at A is projected across the table with velocity u. Find the speed with which the second particle begins to move if the direction of u is :- NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 (i) along BA, (ii) at an angle of 120° with AB (iii) perpendicular to AB. In each case calculate (in terms of m and u) the impulsive tension in the string. 7 . After a completely inelastic collision two objects of the same mass and same initial speed are found to move away together at half their initial speed. Find the angle between the initial velocities of the objects. 8 . A cylindrical solid of mass 10–2 kg and cross–sectional area 10–4 m2 is moving parallel to its axis (the x–axis) with a uniform speed of 103 m/s in the positive direction. At t = 0, its front face passes the plane x = 0. The region to the right of this plane is filled with the dust particle of uniform density 10–3 kg/m3. When a dust particles collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged and that the dust sticks only to the front face of the cylinder find the x–coordinate of the front of the cylinder at t = 150 s. 74 E
JEE-Physics 9 . Two particles each of mass m are connected by a light inextensible string and a particle of mass M is attached to the midpoint of the string. The system is at rest on a smooth horizontal table with the string just taut and in a straight line. The particle M is given a velocity v along the table perpendicular to the string. Prove that Mv when the two particles are about to collide : (i) The velocity of M is M 2m 2M(M m (ii) The speed of each of the other particles is M 2m v. 1 0 . The Atwood machine in figure has a third mass attached to it by a limp string. After being released, the 2m mass falls a distance x before the limp m 2m string becomes taut. Thereafter both the mass on the left rise at the same speed. What is the final speed? Assume that pulley is ideal. m 1 1 . A wedge of mass M=2m rests on a smooth horizontal plane. A small block B 20cm of mass m rests over it at left end A as shown in figure. A sharp impulse is m v0 A M applied on the block, due to which it starts moving to the right with velocity v = 6 ms–1. At highest point of its trajectory, the block collides with a particle 0 of same mass m moving vertically downwards with velocity v = 2 ms–1 and gets stuck with it. If the combined body lands at the end point A of body of mass M, calculate length . Neglect friction (g = 10 ms–2) 1 2 . A ball of mass m=1 kg is hung vertically by a thread =1.50 m. Upper end of the thread is attached to the ceiling of a trolley of mass M = 4 kg. 1.50m M Initially, trolley is stationary and it free to move along horizontal rails without mm friction. A shell of mass m = 1 kg moving horizontally with velocity v0 v =6 ms–1 collides with the ball and gets stuck with it. As a result, thread h2 0 starts to deflected towards right. Calculate its maximum deflection with the vertical. (g = 10 ms–2) B 1 3 . A 70 g ball B dropped from a height h = 9 m A 0 reaches a height h = 0.25 m after bouncing twice 2 from identical 210 g plates. Plate A rests directly h0 on hard ground, while plate C rests on a foam – rubber mat. Determine. (i) the coefficient of restitution between the ball and the plates, NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 (ii) the height h of the ball's first bounce. om 1 M 1 4 . A ball of mass m = 1 kg falling vertically with a velocity v0 = 2 m/s strikes 300 a wedge of mass M = 2 kg kept on a smooth, horizontal surface as shown in figure. The coefficient of resitution between the ball and the wedge is e = 1/2. Find the velocity of the wedge and the ball immediately after collision. BRAIN STORMING SUBJECTIVE EXERCISE ANSWER KEY EXERCISE–4(B) 1. (i) 370 (ii) (120, 45) 2. 44.25 m m2 m1 cot h 4. e=0.8, =0.4 3. m m1 m2 2ag 3v 2v u mu u 3 mu 3 u 3 mu 3 7. 1200 8. 105 m 5. (i) 3 (ii) g (iii) g 6. (i) , (ii) , (iii) , 22 8 8 4 4 3gx 12 10. 11. 40 cm 12. 370 13. (i) 0.66 (ii) 4 m 14. v = ms–1, v = ms–1 13 23 8 E 75
JEE-Physics PREVIOUS YEAR QUESTIONS EXERCISE–05 (A) 1 . Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is- [AIEEE - 2002] (1) v (2) v/3 (3) v/2 (4) zero 2 . Consider the following two statements :- [AIEEE - 2003] A : Linear momentum of a system of particles is zero. B : Kinetic energy of a system of particles is zero. Then- (1) A does not imply B and B does not imply A (2) A implies B but B does not imply A (3) A does not imply B but B implies A (4) A implies B and B implies A 3 . Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. It they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is- [AIEEE - 2003] (1) 2.5 R (2) 4.5 R (3) 7.5 R (4) 1.5 R 4 . A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 12 3 M and, a body C of mass 3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards- [AIEEE - 2005] (1) depends on height of breaking (4) body B (2) does not shift (3) body C 5 . The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is- [AIEEE - 2005] M (1) Mk L kL2 (3) zero M L2 (2) (4) 2M k 6 . A mass m moves with a velocity v and collides inelastically with another identical mass. After collision the Ist mass moves with velocity v in a direction perpendicular to the initial direction of motion. Find the speed of the 3 second mass after collision- [AIEEE-2005] 2v (1) v (2) 3 v (3) v (4) 33 7 . A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A B NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C. P 2 [AIEEE - 2005] F (1) 2 (2) 3 (3) 4 (4) C 3 2 3 8 . A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms–1. The kinetic energy of the other mass is- [AIEEE - 2006] (1) 144 J (2) 288 J (3) 192 J (4) 96 J 9 . Consider a two particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position ? [AIEEE - 2006] (1) m2 d (2) m1 d (3) m1 d (4) d m1 m1 m2 m2 76 E
JEE-Physics 1 0 . A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is R from the centre of the bigger disc. The value of is : - [AIEEE - 2007] (1) 1/3 (2) 1/2 (3) 1/6 (4) 1/4 1 1 . A block of mass 0.50 kg is moving with a speed of 2.00 ms–1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is :- [AIEEE - 2008] (1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J 1 2 . A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. It linear density (mass/length) xn where n can be zero or any positive number. If the position x of the centre of mass of varies with x as k L CM the rod is plotted against ‘n’, which of the following graphs best approximates the depence of xCM on n? [AIEEE - 2008] (1) (2) (3) (4) 1 3 . Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic.Then the velocity as a function of time and the height as a function of time will be :- [AIEEE - 2009] v y v y +v1 h +v1 h (1) O t (2) O t1 2t1 3t1 4t1 t –v1 t1 2t1 3t1 4t1 t –v1 t v y v y +v1 h +v1 h (3) O t t (4) O t –v1 t Directions : This Questions contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best discribes the two statements. NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 1 4 . Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions. [AIEEE - 2010] (1) Statement–1 is true, Statement–2 is false (2) Statement–1 is true, Statement–2 is true; Statement–2 is the correct explanation of Statement–1 (3) Statement–1 is true, Statement–2 is true; Statement–2 is not the correct explanation of Statement–1 (4) Statement–1 is false, Statement–2 is true ANSWER-KEY Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Ans. 3 3 3 2 1 3 3 2 3 1 3 1 1 2 E 77
JEE-Physics EXERCISE–05 (B) PREVIOUS YEAR QUESTIONS MCQ's with one correct answer 1. Two particles of masses m and m in projectile motion have velocities v1 v2 respectively at time t = 0. 12 They collide at time t . Their velocities become v '1 and v '2 at time 2t while still moving in air. The value 0 0 '2 of : [(m v '1 +m v ) – (m v1 +m v2 )] is :– [IIT-JEE 2001] 1 2 1 2 (A) zero (B) (m1 + m1)gt0 (C) 2(m1 + m2)gt0 1 (D) 2 (m1 + m2)gt0 2 . Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is :– [IIT-JEE 2002] (A) 30 m/s (B) 20 m/s (C) 10 m/s (D) 5 m/s 3. A particle moves in the X–Y plane under the influence of a force such that its linear momentum is A[ˆi cos(kt) ˆj sin(kt)] , where A and k are constants. The angle between the force and the momentum p(t) is :– (B) 30° (C) 45° [IIT-JEE 2007] (A) 0° (D) 90° 4 . Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other that at A, these two particles will again reach the point A ? [IIT-JEE 2009] V A 2V (A) 4 (B) 3 (C) 2 (D) 1 5 . Look at the drawing given in the figure which has been drawn with ink of uniform line– thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments in m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0), left inner circle (– a, a) , right inner circle (a, a), vertical line (0, 0) and horizontal line (0, – a). The y–coordinates of the centre of mass of the ink in this drawing is :– [IIT-JEE 2009] y x NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 a a a a (A) (B) (C) (D) 10 8 12 3 6 . A particle of mass m is projected from the ground with an initial speed u0 at an angle with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u . The angle that the composite 0 system makes with the horizontal immediately after the collision is :- [IIT-JEE 2013] (B) (C) 4 2 (A) (D) 4 2 78 E
JEE-Physics MCQ's with one or more than one correct answers 1. Two balls, having linear momenta pˆi and pˆi , undergo a collision in free space. There is no external p1 p2 force acting on the balls. Let p1' and p2' be their final momenta. The following option(s) is (are) NOT ALLOWED for any non–zero value of p, a , a , b , b , c and c . [IIT-JEE 2008] 12 1 21 2 (A) a1ˆi b1ˆj c1kˆ (B) c1kˆ (C) a1ˆi b1ˆj c1kˆ (D) a1ˆi b1ˆj p 1' a2ˆi b2ˆj p1' p1' p1' a2ˆi b1ˆj p2' p2' p2' c2kˆ p2' a2ˆi b2ˆj c2kˆ Assertion – Reason 1 . Statement–1 : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. [IIT-JEE 2007] and Statement–2 : In an elastic collision, the linear momentum of the system is conserved. 2 . Statement–1 : If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant. [IIT-JEE 2007] and Statement–2 : The linear momentum of an isolated system remains constant. Comprehension based questions [IIT-JEE 2008] A small block of mass M moves on a frictionless surface of an inclined plane, as shown in 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) A M v 60° B NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 30° C 3m 3 3m 1 . The speed of the block at point B immediately after it strikes the second incline is :– (A) 60 m/s (B) 45 m/s (C) 30 m/s (D) 15 m/s 2 . The speed of the block at point C, immediately before it leaves the second incline is :– (A) 120 m/s (B) 105 m/s (C) 30 m/s (D) 75 m/s 3 . If 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 :– (A) 30 m/s (B) 15 m/s (C) 0 (D) – 15 m/s E 79
JEE-Physics Subjective Questions 1 . Two blocks of mass 2 kg and M are at rest on an inclined plane and are separated by a distance of 6.0 m as shown. The coefficient of friction between each block and the inclined plane is 0.25. The 2 kg block is given a velocity of 10.0 m/s up the inclined plane. It collides with M, comes back and has a velocity of 1.0 m/s when it reaches its initial position. The other block M after the collision moves 0.5 m up and comes to rest. Calculate the coefficient of restitution between the blocks and the mass of the block M. (Take sin tan = 0.05 and g = 10 m/s2) [IIT-JEE 1999] M 6.0m 2 kg 2 . A car P is moving with a uniform speed of 5 3 m/s towards a carriage of mass 9 kg at rest kept on the rails at a point B as shown in figure. The height AC is 120 m. Cannon balls of 1 kg are fired from the car with an initial velocity 100 m/s at an angle 30° with the horizontal. The first cannon balls hits the stationary carriage after a time t and sticks to it. Determine t . 00 C P AB At t , the second cannon ball is fired. Assume that the resistive force between the rails and the carriage is constant 0 and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks of the carriage, what will be the horizontal velocity of the carriage just after the second impact? [IIT-JEE 2001] 3 . A particle of mass m, moving in a circular path of radius R with a constant speed v2 is located at point (2R, 0) at time t = 0 and a man starts moving with a velocity v along the positive y–axis from origin at time t = 0. Calculate 1 the linear momentum of the particle w.r.t. man as a function of time. [IIT-JEE 2003] y NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 v1 v2 (0,0) R x m 4 . Two point masses m and m are connected by a spring of natural length . The spring is compressed 12 0 such that the two point masses touch each other and then they are fastened by a string. Then the system is moved with a velocity v along positive x–axis. When the system reaches the origin the string breaks 0 (t = 0). The position of the point mass m is given by x = v t–A(1–cos t) where A and are constants. 1 1 0 Find the position of the second block as a function of time. Also find the relation between A and . 0 [IIT-JEE 2003] 80 E
JEE-Physics 5 . There is a rectangular plate of mass M kg of dimensions (a × b). The plate is held in horizontal position by striking n small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity v. What is v ? It is given n=100, M = 3 kg, m=0.01 kg, b=2m, a=1m, g=10 m/s2. [IIT-JEE 2006] b a 6 . Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line Find the final speed (in m/s ) of the object C. [IIT-JEE 2009] B AC m 2m m PREVIOUS YEARS QUESTIONS ANSWER KEY EXERCISE –5 NODE6 E : \\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-3\\Centre of mass & collision\\Eng\\Exercise.p65 MCQ's with one correct answer 1. C 2. C 3. D 4. C 5. A 6. A MCQ's with one or more than one correct answers 1. A,D 3. C 2. 12 s, 15.75 ms–1 Assertion – Reason 1. B 2. D Comprehension Based questions 1. B 2. B Subjective Questions 1. e = 0.84, M = 15.21 kg 3. – mv sin v2 t ˆi + m v 2 cos v2 t v1 ˆj 2 R R m1 m1 m2 A m2 1 A 4. x = v t + 20 0 1 cos t , = 5. 10 ms–1 6. 4 m/s E 81
JEE-Physics EXERCISE–01 CHECK YOUR GRASP SELECT THE CORRECT ALTERNATIVE (ONLY ONE CORRECT ANSWER) 1 . On an X temperature scale, water freezes at –125.0° X and boils at 375.0° X. On a Y temperature scale, water freezes at –70.0° Y and boils at –30.0° Y. The value of temperature on X–scale equal to the temperature of 50.0°Y on Y–scale is :– (A) 455.0°X (B) –125.0°X (C) 1375.0°X (D) 1500.0°X 2 . A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 140°F What is the temperature as registered by the centigrade thermometer :– (A) 30° (B) 40° (C) 60° (D) 80° 3 . The graph AB shown in figure is a plot of temperature of a body in degree 100°C B Celsius and degree Fahrenheit. Then :– (A) Slope of line AB is 9/5 Centigrade (B) Slope of line AB is 5/9 (C) Slope of line AB is 1/9 Fahrenheit (D) slope of line AB is 3/9 32°F 212°F A 4 . Two absolute scales X and Y assigned numerical values 200 and 450 to the triple point of water. What is the relation between T and T ? XY (A) 9TX = 4TY (B) 4TX = 9TY (C) TX = 3TY (D) None of these 5 . A faulty thermometer reads freezing point and boiling point of water as –5°C and 95°C respectively. What is the correct value of temperature as it reads 60°C on faulty thermometer? (A) 60°C (B) 65°C (C) 64°C (D) 62°C 6 . A steel scale is to be prepared such that the millimeter intervals are to be accurate within 6 × 10–5 mm. The maximum temperature variation during the ruling of the millimeter marks is (=12×10–6C–1):– (A) 4.0°C (B) 4.5°C (C) 5.0°C (D) 5.5°C. 7 . A meter washer has a hole of diameter d and external diameter d , where d =3d . On heating, d increases by 1 2 21 2 0.3%. Then d will :– 1 (A) decrease by 0.1% (B) decrease by 0.3% (C) increase by 0.1% (D) increase by 0.3%. 8 . At 4°C, 0.98 of the volume of a body is immersed in water. The temperature at which the entire body gets immersed in water is (neglect the expansion of the body) (w 3.3 104 K 1 ) :– (A) 40.8°C (B) 64.6°C (C) 60.6°C (D) 58.8°C 9 . Two metal rods of the same length and area of cross–section are fixed ends to end between rigid supports. The materials of the rods have Young moduli Y1 and Y2, and coefficients of linear expansion 1 and 2. When \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 rods are cooled the junction between the rods does not shift if:– (A) Y11 = Y22 (B) Y12 = Y21 (C) Y11 = Y22 (D) Y11 = Y22 1 0 . In a vertical U–tube containing a liquid, the two arms are maintained at different temperatures, t1 and t2. The liquid columns in the two arms have heights 1 and 2 respectively. The coefficient of volume expansion of the liquid is equal to:– 2 t2 t1 1 1 2 1 2 1 2 1 2 (A) 2 t1 1 t2 (B) 1 t1 2 t2 (C) 2 t1 1 t2 (D) 1 t1 2 t2 90 E
JEE-Physics 1 1 . A steel rod of length 1 m is heated from 25°C to 75°C keeping its length constant. The longitudinal strain developed in the rod is:– (Given : Coefficient of linear expansion of steel = 12 x 10–6/°C) (A) 6 × 10–6 (B) –6 × 10–5 (C) –6 × 10–4 (D) zero 1 2 . A brass disc fits simply in a hole of a steel plate. The disc from the hole can be loosened if the system (brass > steel) (A) First heated then cooled (B) First cooled then heated (C) Is heated (D) Is cooled 1 3 . The variation of lengths of two metal rods A and B with change in temperature is shown in figure. The ratio A of B is:– 106 length(cm) 104 B 100 A 3 2 0T 3 (A) (B) temp. (°C) (D) 2 3 4 4 (C) 3 1 4 . A steel tape is placed around the earth at the equator when the temperature is 10°C. What will be the clearance between the tape and the ground (assumed to be uniform) if the temperature of the tape rises to 40°C ? Neglect expansion of the earth. Radius of earth at equator is 6400 km & steel = 1.2 × 10–5 K–1 (A) 2.3 m (B) 2.1 m (C) 2.3 km (D) 230 m 1 5 . Bars of two different metals are bolted together, as shown in figure.The distance x does not change with temperature if:– A A B B (A) A A (B) A B (C) 2A A (D) 2A B B B B A 2B B 2B A 16. A metal rod A of length expands by when its temperature is raised by 100°C. Another rod B of different 0 for same rise in temperature. A third rod C of length 3 is made metal of length 2 by /2 expands 00 up of pieces of rods A and B placed end to end expands by 2 on heating through 100 K. The length \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 of each portion of the composite rod is:– (A) 5 , 4 (B) , 2 (C) 30 , 30 (D) 2 0 , 7 0 30 30 00 22 3 3 1 7 . The coefficient of linear expansion '' of a rod of length 2m varies with the distance x from the end of the rod as = 0 + 1x where 0 = 1.76 × 10–5 °C–1 and 1 = 1.2 × 10–6m–1 °C–1. The increase in the length of the rod, when heated through 100°C is:– (A) 2cm (B) 3.76mm (C) 1.2 mm (D) None of these 18. The coefficient of linear expansion of the material of a rod of length varies with absolute temperature as 0 =aT – bT2 where a & b are constants. The linear expansion of the rod when heated from T to T = 2T is:– 1 2 1 (A) 3 a T12 7b T13 L 0 (B) 4a 7b T1 L 0 (C) 2 a T12 7b T13 L 0 (D) None of these 2 3 3 3 E 91
JEE-Physics 1 9 . A clock with a metallic pendulum gains 6 seconds each day when the temperature is 20°C and loses 6 second when the temperature is 40°C. Find the coefficient of linear expansion of the metal. (A) 1.4 × 10–5 °C–1 (B) 1.4 × 10–6 °C–1 (C) 1.4 × 10–4 °C–1 (D) 0.4 × 10–6 °C–1 2 0 . A steel scale measures the length of a copper rod as when both are at 20°C, which is the calibration tempera- 0 ture for the scale. The scale reading when both are at 40°C, is:– (A) 1 20C 0 (B) 1 20S 0 (C) 1 20S 0 (D) 1 20 C 0 1 20C 1 20 S 2 1 . The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are 1 and 2 respectively. If the coefficient of linear expansion of the vessel A is 1, the coefficient of linear expansion of the vessel B is:– 11 2 1 2 (C) 1 2 (D) 1 2 31 (A) 1 2 (B) 21 3 3 2 2 . Three rods of the same dimensions have thermal conductivities 3k, 2k and k. They are arranged as shown, with their ends at 100°C, 50°C and 0°C. The temperature of their junction is:– 50°C 100°C 2k 3k k 0°C (A) 75°C (B) 200 C (C) 40°C (D) 100 C 3 3 2 3 . A cup of tea cools from 80°C to 60°C in one minute. The ambient temperature is 30°C. In cooling from 60°C to 50°C. It will take :– (A) 50 s (B) 90 s (C) 60 s (D) 48 s 2 4 . Ice starts forming in lake with water at 0°C when the atmospheric temperature is –10°C. If the time taken for 1 cm of ice be 7 hours, then the time taken for the thickness of ice to change from 1 cm to 2 cm is :– (A) 7 hours (B) 14 hours (C) less than 7 hours (D) more than 7 hours 2 5 . There is a small hole in a container. At what temperature should it be maintained in order that it emits one calorie of energy per second per meter2 :– (A) 10K (B) 500K (C) 200K (D) 100K 2 6 . A blackened metallic foil is kept at a distance d from a spherical heater. The power absorbed by the foil is P. If \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 the temperature of heater and distance both are doubled, then the power absorbed by the foil will be:– (A) 8P (B) 4P (C) 2P (D) P 2 7 . Two different rods A and B are kept as shown in figure. The variation of temperature of different cross sections with distance is plotted in a graph shown in figure. The ratio of thermal conductivities of A and B is- Temp.(°C) 100° 100°C 70°C 35°C 70° A B 35° (A) 2 (B) 0.5 0 30 Distance 100 (cm) (C) 1 (D) 2/3 92 E
JEE-Physics 28. The area of cross–section of rod is given by A = A (1 + x) where A & are constant and x is the distance from one end. 0 0 resistance of the rod if its length is ? If the thermal conductivity of the material is K, what is the thermal 0 (A) KA0 n(1 + 0) (B) 1 n (1 0 ) (C) n (1 0 ) (D) KA 0 n (1 0 ) A0 KA K 0 2 9 . Which of the following graph shows the correct variation in intensity of heat radiations by black body and frequency at a fixed temperature:– E E E E UV Visible Infra-red UV Visible Infra-red Infra-red Visible Ultra-voilet Infra-red Visible Ultra-voilet 3500K 3500K 1500K 2500K 1500K (D) 2500K 3500K (A) (B) 2500K (C) 2500K 1500K 1500K 3500K 3 0 . A red star and a green star radiate energy at the same rate which star is bigger. (A) Red (B) Green (C) Both have same size (D) Can't be say anything 3 1 . 250 g of water and an equal volume of alcohol of mass 200 g are placed successively in the same calorimeter and cools from 60°C to 55°C in 130 sec and 67 sec respectively. If the water equivalent of the calorimeter is 10 g then the specific heat of alcohol in cal/g°C is :– (A) 1.30 (B) 0.67 (C) 0.62 (D) 0.985 3 2 . The weight of a person is 60 kg. If he gets 10 calories of heat through food and the efficiency of his body is 28%, then upto what height he can climb ? Take g = 10 m s–2 (A) 100 cm (B) 1.96 cm (C) 400 cm (D) 1000 cm 3 3 . Two identical masses of 5 kg each fall on a wheel from a height of 10m. The wheel disturbs a mass of 2 kg water, the rise in temperature of water will be :– (A) 2.6° C (B) 1.2° C (C) 0.32° C (D) 0.12° C 3 4 . Hailstone at 0°C falls from a height of 1 km on an insulating surface converting whole of its kinetic energy into heat. What part of it will melt:– [g = 10 m/s2, Lice = 330 × 103 J kg–1] 1 1 (C) 1 10 4 (D) All of it will melt (A) 33 (B) 8 33 3 5 . If H , H and H are heat required to raise the temperature of one gram of water by one degree in Celsius, CK F Kelvin and Fahrenheit temperature scales respectively then :– \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 (A) H > H > H (B) H > H > H (C) H = H > H (D) H = H = H KCF FCK KCF KCF 36. Steam at 100°C is passed through 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at 15°C till the temperature of the calorimeter and its contents rises to 80°C. The mass of the steam condensed in kg is :– (A) 0.130 (B) 0.065 (C) 0.260 (D) 0.135 3 7 . Water is used to cool the radiators of engines in cars because :– (A) of its low boiling point (B) of its high specific heat (C) of its low density (D) of its easy availability 3 8 . If mass–energy equivalence is taken into account, when water is cooled to form ice, the mass of water should:– (Note : The mass energy of an object is the energy equivalent of its mass, as given by E = mc2, where m = mass of object & c = speed of light) (A) increase (B) remain unchanged (C) decrease (D) first increase then decrease E 93
JEE-Physics 3 9 . If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5 kg. water at standard temperature and pressure will be given by :– (A) 5.6 m3 (B) 4.5 m3 (C) 11.2 litre (D) 11.2 m3 4 0 . A refrigerator converts 100 g of water at 25°C into ice at – 10°C in one hour and 50 minutes. The quantity of heat removed per minute is:– (Specific heat of ice = 0.5 cal/g°C, latent heat of fusion = 80 cal/g) (A) 50 cal (B) 100 cal (C) 200 cal (D) 75 cal 4 1 . Pressure versus temperature graphs of an ideal gas are as shown in figure. Choose the wrong statement:– PPP (i) (ii) (iii) T TT (A) Density of gas is increasing in graph (i) (B) Density of gas decreasing in graph (ii) (C) Density of gas is constant in graph (iii) (D) None of the above 4 2 . In a process the density of a gas remains constant. If the temperature is doubled, then the change in the pressure will be:– (A) 100 % increase (B) 200 % increase (C) 50 % decrease (D) 25 % decrease 4 3 . The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here:– a Ob (A) a = volume, b = °C temperature (B) a = volume, b = K temperature (C) a = °C temperature, b = volume (D) a = K temperature, b = volume 1 4 4 . Air is filled at 60° C in a vessel of open mouth. The vessel is heated to a temperature T so that th part of air 4 escapes. The value of T is :– (A) 80° C (B) 444° C (C) 333° C (D) 171° C 45. One mole of an ideal gas undergoes a process P P0 Here P and V are constants. Change in 00 1 (V0 / V )2 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 temperature of the gas when volume is changed from V =V to V = 2V is :– 00 (A) 2P0 V0 (B) 11P0 V0 (C) 5P0 V0 (D) P0 V0 5R 10R 4R 4 6 . Two identical glass bulbs are interconnected by a thin glass tube at 0ºC. A gas is filled at N.T.P. in these bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times. The temperature of hot bath will be :– Ice Hot water (A) 100°C (B) 182°C (C) 256°C (D) 546°C 94 E
JEE-Physics 4 7 . A gas has volume V and pressure P. The total translational kinetic energy of all the molecules of the gas is:– 3 3 (A) PV only if the gas is monoatomic. (B) PV only if the gas is diatomic. 2 2 3 3 (C) > PV if the gas is diatomic. (D) PV in all cases. 2 2 48. A mixture of n1 moles of monoatomic gas and n2 moles of diatomic gas has CP 1.5 :– CV (A) n1 = n2 (B) 2n1 = n2 (C) n1 = 2n2 (D) 2n1 = 3n2 4 9 . Four containers are filled with monoatomic ideal gases. For each container, the number of moles, the mass of an individual atom and the rms speed of the atoms are expressed in terms of n, m and v respectively. If T , T ,T rms A B C and T are their temperatures respectively then which one of the options correctly represents the order ? D ABCD Number of moles n 3n 2n n Mass 4m m 3m 2m Rms speed v rms 2v rms v rms 2v rms Temperature TA TB TC TD (A) T = T > T > T (B) T > T > T > T (C) T > T = T > T (D) T > T > T > T BCAD DACB DABC BCA D 5 0 . 1023 molecules of a gas strike a target of area 1 m2 at angle 45° to normal and rebound elastically with speed 1 kms–1. The impulse normal to wall per molecule is:– [Given : mass of molecule = 3.32 × 10–27kg] (A) 4.7 × 10–24 kg ms–1 (B) 7.4 × 10–24 kg ms–1 (C) 3.32× 10–24 kg ms–1 (D) 2.33 kg ms–1 5 1 . From the following V–T diagram we can conclude:– V P2 P1 (A) P = P (B) P >P T1 T2 T (D) Can't say anything 12 12 (C) P < P 12 5 2 . The density in grams per litre of ethylene (C H ) at STP is :– 24 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 (A) 1.25 (B) 2.50 (C) 3.75 (D) 5.25 5 3 . A gas is expanded from volume V to 2V under three different processes. Process 1 is isobaric process, 00 process 2 is isothermal and process 3 is adiabatic. Let U1, U and U3, be the change in internal energy 2 of the gas is these processes. Then :– P 1 P0 2 3 V V0 2V0 (A) U1 > U2 > U3 (B) U1 < U2 < U3 (C) U2 < U1 < U3 (D) U2 < U3 < U1 E 95
JEE-Physics 5 4 . Some of the thermodynamic parameters are state variables while some are process variables. Some grouping of the parameters are given. Choose the correct one. (A) State variables : Temperature, No of moles Process variables : Internal energy, work done by the gas. (B) State variables : Volume, Temperature Process variables : Internal energy, work done by the gas. (C) State variables : Work done by the gas, heat rejected by the gas Process variables : Temperature, volume. (D) State variables : Internal energy, volume Process variables : Work done by the gas, heat absorbed by the gas. 5 5 . For an ideal gas PT11 = constant then volume expansion coefficient is equal to :– 11 1 12 2 (A) (B) (C) (D) T T T T 5 6 . The internal energy of a gas is given by U = 5 + 2PV. It expands from V to 2V against a constant pressure P . 00 0 The heat absorbed by the gas in the process is :– (A) –3P V (B) 3P V (C) 2P V (D) P V 00 00 00 00 5 7 . When water is heated from 0°C to 4°C and C and C are its specific heats at constant pressure and constant PV volume respectively, then :– (A) C > C (B) C < C (C) C = C (D) C – C = R PV PV PV PV 5 8 . The molar specific heat of the process V T4 for CH4 gas at room temperature is:– (A) 4R (B) 7R (C) 3R (D) 8R 5 9 . 5n, n and 5n moles of a monoatomic, diatomic and non-linear polyatomic gases (which do not react chemically with each other) are mixed at room temperature. The equivalent degree of freedom for the mixture is :– 25 48 52 50 (A) 7 (B) 11 (C) 11 (D) 11 6 0 . The internal energy of a gas in an adiabatic process is given by U = a + bPV, find :– a 1 b 1 b 1 a (A) (B) (C) (D) a b a b 1 CHECK YOUR GRASP ANSWER KEY EXERCISE –1 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ans. C C B A B C D B A A C D B C B A B A A D Que. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ans. D B D D D B B B C A C B D A C D B C A B Que. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Ans. D A C D B D D A C A C A A D C B B B D B 96 E
JEE-Physics EXERCISE–02 BRAIN TEASURES Select the correct alternatives (one or more than one correct answers) 1 . A triangular plate has two cavities, one square and one rectangular as shown in figure. The plate is heated. a a b b x (B) a and b both increase (D) a, b, x and all increase (A) a increase, b decrease (C) a and b increase, x and decrease 2 . Three rods of equal length are joined to form an equilateral triangle ABC.D is the midpoint of AB. The coefficient of linear expansion is 1 for AB, and 2 for AC and BC. If the distance DC remains constant for small changes in temperature:– A D 1 B 2 2 C (A) 1 = 2 (B) 1 = 22 (C) 1 = 42 1 (D) 1 = 2 2 3 . If water at 0°C, kept in a container with an open top, is placed in a large evacuated chamber:– (A) All the water will vaporize. (B) All the water will freeze. (C) Part of the water will vaporize and the rest will freeze. (D) Ice, water and water vapour will be formed and reach equilibrium at the triple point. 4 . In the previous question, if the specific latent heat of vaporization of water at 0°C is times the specific latent heat of freezing of water at 0°C, the fraction of water that will ultimately freeze is:– 1 1 1 (A) (B) 1 (C) (D) 1 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 5 . Which of the following statements is/are correct ? (A) A gas has two specific heats only (B) A material will have only one specific heat, if and only if its coefficient of thermal expansion is equal to zero. (C) A gas has infinite number of specific heats. (D) None of these 6 . When two samples at different temperatures are mixed, the temperature of the mixture can be :– (A) lesser than lower or greater than higher temperature (B) equal to lower or higher temperature (C) greater than lower but lesser than higher temperature (D) average of lower and higher temperatures. 7 . Two identical beakers are filled with water to the same level at 4°C. If one say A is heated while the other B is cooled, then:– (A) water level in A will rise (B) water level in B will rise (C) water level in A will fall (D) water level in B will fall E 97
JEE-Physics 8 . The figure shows two paths for the change of state of a gas from A to B. The ratio of molar heat capacities in path 1 and path 2 is:– P 2 B A 1 V (A) > 1 (B) < 1 (C) 1 (D) Data insufficient 9 . During the melting of a slab of ice at 273 K at atmospheric pressure:– (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 ice–water system increases. (D) The internal energy of the ice–water system decreases. 1 0 . Two substances A and B of equal mass m are heated by uniform rate of 6 cal s–1 under similar conditions. A graph between temperature and time is shown in figure. Ratio of heat absorbed H /H by them for complete AB fusion is:– 100 80 A 60 40 B 20 01 2 3 45 6 7 Time(s) Temperature (°C) 9 4 8 5 (A) (B) 9 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65(C) 5(D) 8 4 1 1 . Three closed vessels A, B and C at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contains only O2, B only N2 and C a mixture of equal quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v1, that of the N2 molecules in vessel B is v , the average speed of O molecules in vessel C is where M is the mass of an oxygen molecule:– 22 (A) (v +v ) /2 (B) v (C) (v v )1/2 (D) 3kT / M 12 1 12 1 2 . A partition divides a container having insulated walls into two compartments I and II.The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position ? P,V,T 2P,2V,T I II (A) The pressure in the two compartments are equal. 3V (B) Volume of compartment I is 5 12V 5P (C) Volume of compartment II is 5 (D) Final pressure in compartment I is 3 98 E
JEE-Physics 1 3 . During experiment, an ideal gas is found to obey a condition P2/= constant [ = density of the gas]. The gas is initially at temperature T, pressure P and density . The gas expands such that density changes to /2 (A) The pressure of the gas changes to 2 P (B) The temperature of the gas changes to 2 T (C) The graph of the above process on the P–T diagram is parabola (D) The graph of the above process on the P–T diagram is hyperbola 1 4 . An ideal gas can be expanded from an initial state to a certain volume through two different processes (i) PV2 = constant and (ii) P = KV2 where K is a positive constant. Then:– (A) Final temperature in (i) will be greater than in (ii) (B) Final temperature in (ii) will be greater than in (i) (C) Total heat given to the gas in (i) case is greater than in (ii) (D) Total heat given to the gas in (ii) case is greater than in (i) 1 5 . Pressure versus temperature graph of an ideal gas is shown in figure.Density of the gas at point A is . Density at B will be:– 0 P 3P0 B P0 A 3 3 T0 2T0 T (D) 20 (A) 4 0 (B) 2 0 4 (C) 3 0 1 6 . When unit mass of water boils to become steam at 1000C, it absorbs Q amount of heat. The densities of water and steam at 1000C are 1 and 2 respectively and the atmospheric pressure is P . The increase in internal 0 energy of the water is:– (A) Q (B) Q P0 1 1 (C) Q P0 1 1 (D) Q P0 1 1 1 2 2 1 1 2 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 1 7 . At temperature T,N molecule s of gas A each havi ng mass m and at the same temperature 2 N molecules of gas B each having mass 2 m are filled in a container. The mean square velocity of molecules of gas B is v2 and x component of mean square velocity of molecules of gas A is w2. The ratio of w2 / v2 is :– (A) 1 (B) 2 (C) 1/3 (D) 2/3 1 8 . A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left (L) and right (R) halves. The rms speed of the molecules in L part is equal to the mean speed of molecules in the R part. Then the ratio of the mass of a molecule in L part to that of a molecule in R part is:– LR 3 (B) / 4 (C) 2 / 3 (D) 3/8 (A) 99 2 E
JEE-Physics 1 9 . A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A contained in the vessel is 2 times that of B. Which of the following statements are true? (A) Average kinetic energy per molecule of A is equal to that of B (B) Root mean square value of translational velocity of B is four times that of A (C) Pressure exerted by B is eight times of that exerted by A (D) Number of molecules of B in the cylinder is eight times that of A 2 0 . N(<100) molecules of a gas have velocities 1,2,3.... N, km/s respectively. Then:– (A) rms speed and average speed of molecules are same (B) Ratio of rms speed to average speed is 2N 1 N 1 6N (C) Ratio of rms speed to average speed is 2N 1 N 1 6 2 2N 1 (D) Ratio of rms speed to average speed of a molecule 6 N 1 2 1 . Let v , vrms and vp respectively denote the mean speed, the root–mean–square speed, and the most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m:– (A) No molecule can have speed greater than vrms vp (B) No molecule can have speed less than 2 (C) v p v v rms (D) The average kinetic energy of a molecule is 3 m v 2 4 p 2 2 . The following are the P–V diagrams for cyclic processes for a gas. In which of these processes is heat absorbed by the gas ? (A) P (B) V (C) P (D) V V P V P 2 3 . The internal energy of a system remains constant when it undergoes :– (A) a cyclic process (B) an isothermal process (C) an adiabatic process \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 (D) any process in which the heat given out by the system is equal to the work done on the system 2 4 . CP is always greater than CV due to the fact that :– (A) No work is being done on heating the gas at constant volume. (B) When a gas absorbs heat at constant pressure its volume must change so as to do some external work. (C) The internal energy is a function of temperature only for an ideal gas. (D) For the same rise of temperature, the internal energy of a gas changes by a smaller amount at constant volume than at constant pressure. 2 5 . An ideal gas is heated from temperature T to T under various conditions. The correct statement(s) is/are:– 12 (A) U = nC (T – T) for isobaric, isochoric and adiabatic process V 2 1 (B) Work is done at expense of internal energy in an adiabatic process and both have equal values (C) U = 0 for an isothermal process (D) C = 0 for an adiabatic process 100 E
JEE-Physics 2 6 . The indicator diagram for two process 1 and 2 carried on an ideal gas is shown in figure.If m1 and m2 be the dP slopes dV for process 1 and process 2 respectively, then:– AP Process 1 Process 2 V O (A) m =m (B) m >m (C) m <m (D) m C =m C 12 12 12 2V 1P 2 7 . An ideal monoatomic gas undergoes a cycle process ABCA as shown in the fig. The ratio of heat absorbed during AB to the work done on the gas during BC is:– V B 2V0 A C V0 ET T0 2T0 5 5 5 5 (A) 2 n 2 (B) (C) 4 n 2 (D) 3 6 2 8 . Logarithms of readings of pressure and volume for an ideal gas were plotted on a graph as shown in Figure. By measuring the gradient, It can be shown that the gas may be :– 2.38 2.30 2.20 2.10 1.10 1.20 1.30 log V (dm3) (A) Monoatomic and undergoing an adiabatic change. (B) Monoatomic and undergoing an isothermal change. (C) Diatomic and undergoing an adiabatic change. (D) Triatomic and undergoing an isothermal change. \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 log P(kPa) 2 9 . A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system is :– P 3P0 C B 2P0 O P0 A D V0 2V0 V (A) P V (B) 2P V (C) P0 V0 (D) zero 00 00 2 E 101
JEE-Physics 3 0 . A thermally insulated chamber of volume 2V is divided by a frictionless piston of area S into two 0 equal parts A and B. Part A has an ideal gas at pressure P and temperature T and in part B is 00 vacuum. A massless spring of force constant k is connected with piston and the wall of the container as shown. Initially spring is unstretched. Gas in chamber A is allowed to expand. Let in equilibrium spring is compressed by x . Then:– 0 B A (A) Final pressure of the gas is kx06 1 S (B) Work done by the gas is kx2 20 1 (C) Change in internal energy of the gas is kx2 (D) Temperature of the gas is decreased. 20 3 1 . One mole of an ideal monatomic gas is taken from A to C along the path ABC. The temperature of the gas at A is T . For the process ABC :– 0 P C 2P0 P0 B A V0 2V0 V (A) Work done by the gas is RT 0 11 (B) Change in internal energy of the gas is 2 RT0 11 13 (C) Heat absorbed by the gas is 2 RT0 (D) Heat absorbed by the gas is 2 RT0 3 2 . The specific heat s of a gas are C =0.2 cal/g °C & C = 0.15 cal/g °C. [ Take R=2 cal/mole0 C ] PV (A) The molar mass of the gas is 40 g (B) The molar mass of the gas cannot be determined from the data given (C) The number of degrees of freedom of the gas molecules is 6 (D) The number of degrees of freedom of the gas molecules is 8 3 3 . Two cylinders A and B fitted with piston contain the equal amount of an ideal diatomic gas at 300K. The piston \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 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, then the rise in the temperature of the gas in B is:– (A) 30 K (B) 10 K (C) 50 K (D) 42 K 3 4 . One mole of an ideal gas at an initial temperature of T K does 6 R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be:– (A) (T + 2.4) K (B) (T – 2.4) K (C) (T + 4) K (D) (T – 4) K 3 5 . One mole of ideal gas undergoes a cyclic process ACBA as shown in figure. Process AC is adiabatic. The temperatures at A, B and C are 300, 600 and 450K respectively:– A (A) In process CA change in internal energy is 225R. (B) In process AB change in internal energy is –150R. (C) In process BC change in internal energy is –225R. P C (D) Change in internal energy during the whole cyclic process is +150R. B 102 V E
JEE-Physics 3 6 . A gas expands such that its initial and final temperatures are equal. Also, the process followed by the gas traces a straight line on the P–V diagram :– (A) The temperature of the gas remains constant throughout. (B) The temperature of the gas first increases and then decreases. (C) The temperature of the gas first decreases and then increases. (D) The straight line has a negative slope. 3 7 . A gas takes part in two processes in which it is heated from the same initial state 1 to the same final tempera- ture. The processes are shown on the P–V diagram by the straight line 1–2 and 1–3.2 and 3 are the points on the same isothermal curve. Q and Q are the heat transfer along the two processes. Then :– 12 P 2 Q1 isothermal 1 Q2 3 V (A) Q1 = Q2 (B) Q1 < Q2 (C) Q1>Q2 (D) insufficient data 3 8 . Radiation from a black body at the thermodynamic temperature T is measured by a small detector at distance 1 d from it. When the temperature is increased to T and the distance to d , the power received by the detector 1 22 is unchanged. What is the ratio d /d ? 21 T2 (B) T2 2 (C) T1 2 (D) T2 4 (A) T1 T1 T2 2 T1 3 9 . A point source of heat of power P is placed at the center 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 the inner surface of the shell is not to exceed T, then the thickness of the shell should not be less than :– 2R 2kT 4 R 2 kT R 2kT R 2kT (A) (B) (C) (D) P P P 4P 4 0 . A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has maximum intensity is . If at another temperature T' the power radiated is 'P' 0 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 and wavelength at maximum intensity is 0 then:– 2 (A) P' T' = 32 PT (B) P' T' = 16 PT (C) P' T' = 8 PT (D) P' T' = 4 PT 4 1 . The emissive power of a black body at T=300 K is 100 Watt/m2. Consider a body B of area A = 10 m2, coefficient of reflectivity r = 0.3 and coefficient of transmission t=0.5. Its temperature is 300 K. Then which of the following is incorrect:– (A) The emissive power of B is 20 W/m2 (B) The emissive power of B is 200 W/m2 (C) The power emitted by B is 200 Watt (D) The emissivity of B is = 0.2 4 2 . A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of 227°C and suspended inside a box whose walls are at a temperature of 27°C. The maximum rate at which its temperature will fall is:– (Take e = 1, Stefan's constant = 5.8 x 10–8 Wm–2 K–4 and specific heat of the metal s = 90 cal/kg/deg, J = 4.2 J/Calorie) (A) 0.055 °C/s (B) 0.066 °C/s (C) 0.044 °C/s (D) 0.03 °C/s E 103
JEE-Physics 4 3 . A hollow copper sphere & a hollow copper cube of same surface area & negligible thickness , are filled with warm water of same temperature and placed in an enclosure of constant temperature , a few degrees below that of the bodies . Then in the beginning :– (A) The rate of energy lost by the sphere is greater than that by the cube (B) The rate of energy lost by the two are equal (C) The rate of energy lost by the sphere is less than that by the cube (D) The rate of fall of temperature for sphere is less than that for the cube . 4 4 . Two long, thin, solid cylinders are identical in size, but they are made of different substances with two different thermal conductivities. The two cylinders are connected in series between a reservoir at temperature T and a reservoir at hot temperature Tcold. The temperature at the boundary between the two cylinders is Tb. One can conclude that:– (A) T is closer to T than it is to T . b hot cold (B) T is closer to T than it is to T . b cold hot (C) T is closer to the temp. of the reservoir that is in contact with the cylinder with the lower thermal conductivity. b (D) T is closer to the temp. of the reservoir that is in contact with the cylinder with the higher thermal conductivity. b 4 5 . A body cools in a surrounding which is at a constant temperature of 0. Assume that it obeys Newton's law of cooling. Its temperature is plotted against time t. Tangent are drawn to the curve at the points P( =2) and Q( =1). These tangents meet the time axis at angles of 2 and 1 as shown, then:– 2 P 1 Q 0 t (A) tan 2 1 0 (B) tan 2 2 0 (C) tan 1 1 (D) tan 1 2 tan 1 2 0 tan 1 1 0 tan 2 2 tan 2 1 4 6 . A spherical body with an initial temperature T is allowed to cool in surroundings at temperature T (<T ). The mass 1 01 of the body is m, its gram specific heat is c, density , area A. If be the Stefan’s constant then the temperature T of the body at time t can be best represented by:– (A) T = (T –T ) e–kt where k 12AT03 (B) T = ( T –T ) n (kt) where k AT0 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 10 rc mc3 1 0 (C) T = T + (T –T ) e–kt where k 12T03 (D) T = T e–kt –T where k AT03 0 10 rc 10 rc 4 7 . A rod of length L with sides fully insulated is of a material whose thermal conductivity varies with temperature as is a constant. The ends of the rod are kept at temperature T and T . The temperature T at x, K= , where 12 T where x is the distance from the end whose temperature is T is:– 1 x x n T2 L T1 T2 L T2 x (D) T + T2 T1 x T1 1L (A) T1 (B) (C) T1e T1L 104 E
JEE-Physics 4 8 . A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T and T constant. The heat carried increases to 12 ACB 2H. What should be the conductivity of the new ADB part? Given ADB = 3 C T1 A B T2 D 7 (B) 2k 5 (D) 3k (A) k (C) k 3 2 4 9 . Twelve conducting rods form the sides of a uniform cube of side . If in steady state, B and H ends of the cube are at 1000C and 00C respectively. Find the temperature of the junction 'A' :– F G 00C E H 1000C C B D A (C) 400C (A) 800C (B) 600C (D) 700C 5 0 . Radius of a conductor increases uniformly from left end to right end as shown in Fig. Material of the conductor is isotropic and its curved surface is thermally isolated from surrounding. Its ends are maintained at temperatures T and T (T > T ). If, in steady state, heat flow rate is equal to H, then which of the following 1 21 2 graphs is correct ? T1 T2 x \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 H H H H x (A) (B) (C) (D) O xO xO xO 5 1 . A sphere of ice at 00C having initial radius R is placed in an environment having ambient temperature > 00C. The ice melts uniformly, such that shape remains spherical. After a time 't' the radius of the sphere has reduced to r. Which graph best depicts r(t) r rr r R R R R (A) (B) c) (D) t t t t E 105
JEE-Physics 5 2 . Three identical rods AB, CD and PQ are joined as shown. P and Q are mid points of AB 00C 300C and CD respectively. Ends A, B, C and D are maintained at 00C, 1000C, 300C and 600C A C respectively. The direction of heat flow in PQ is:– (A) From P to Q (B) From Q to P PQ (C) Heat does not flow in PQ (D) Data not sufficient BD 1000C 1 1 600C 5 3 . Three bodies A, B and C have equal surface area and thermal emissivities in the ratio e : e : e = 1 : : . All ABC 24 the three bodies are radiating at same rate. Their wavelengths corresponding to maximum intensity are A , B and C respectively and their temperatures are T , T and T on kelvin scale, then select the incorrect statement AB C (A) TA TC =T (B) A C B (C) e A TA e C TC =e T (D) e A A TA .e B B TB = e CC TC B BB 5 4 . A and B are two points on a uniform metal ring whose centre is C. The angle ACB = . A and B maintained at two different constant temperatures. When = 180°, the rate of total heat flow from A to B is 1.2 W. When = 90°, this rate will be:– (A) 0.6 W (B) 0.9 W (C) 1.6 W (D) 1.8 W 5 5 . In a 10–metre–deep lake, the bottom is at a constant temperature of 4°C. The air temperature is constant at –4°C. The thermal conductivity of ice is 3 times that of water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be:– (A) 7.5 m (B) 6 m (C) 5 m (D) 2.5 m 5 6 . The solar constant for the earth is . The surface temperature of the sun is T K. The sun subtends an angle at the earth:– (A) T4 (B) T2 (C) 2 (D) 5 7 . A system S receives heat continuously from an electrical heater of power 10W. The temperature of S becomes constant at 50°C when the surrounding temperature is 20°C. After the heater is switched off, S cools from 35.1°C to 34.9°C in 1 minute. The heat capacity of S is:– (A) 100 J/°C (B) 300 J/°C (C) 750 J/°C (D) 1500 J/°C 5 8 . If the absorption coefficient and reflection coefficient of a surface of a body are 0.4 and 0.6 respectively then:– (A) Emissive power will be 0.2 (B) Transmission power will be 0.2 (C) Body will be totally transparent (D) Body will be totally opaque. 5 9 . Temperature of black body is 3000K when black body cools, then change in wevelength = 9 micron corresponding to maximum energy density. Now temperature of black body is :– (A) 300 K (B) 2700 K (C) 270 K (D) 1800 K \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 6 0 . Two Plates of equal areas are placed in contact with each other. Their thickness are 2cm and 3cm respectively. Temperature of external surface of first plate is –25° C and that of external surface of second plate is 25° C What will be temperature of contact surface if the plates :– (i) Are of same material (ii) Have thermal Conductivity in ratio 2 : 3. (A) (i) –5°C (ii) 0°C (B) (i) 5°C (ii) 0°C (C) (i) 0°C (ii) –5°C (D) None of these 6 1 . Two identical square rods of metal are welded end to end as shown in figure (a) 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in :– 0°C 100°C 0°C 100°C (A) 1 minute (D) 16 minutes (a) (b) (B) 2 minutes (C) 4 minutes 106 E
JEE-Physics 6 2 . Three rods of same dimensions are arranged as shown in the figure. They have thermal C conductivities k , k & k . The points A and B are maintained at different temperatures. k2 12 3 B For the heat to flow at the same rate along ACB and AB :– k3 (A) k3 = 2(k1 + k2) k1k2 k1 (B) k3 = k1 k 2 A (C) k = k + k 1 312 (D) k = (k + k ) 3 21 2 6 3 . The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T and T (T > T ). The rate of 2 12 1 heat transfer through the slab, in a steady state is A ( T2 T1 )K f, with f equals to:– x x 4x T2 K 2K T1 (A) 1 (B) 1/2 (C) 2/3 (D) 1/3 6 4 . The figure shows a system of two concentric spheres of radii r and r and kept at temperatures T and 12 1 T , respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional 2 to:– r1 • T1 r2 T2 (A) (r2 r1 ) (B) n r2 (C) r1r2 (D) (r – r ) (r1r2 ) r1 (r2 r1) 21 65. The pressure of one mole of an ideal gas varies according to the law P P0 aV 2 , where P and a are positive 0 constants. The highest temperature that the gas may attain is:– 2 P0 P0 1/2 3 P0 P0 1/2 P0 P0 1 / 2 P0 P0 1/2 3R 3a 2R 3a R 3a R 3a \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65(A)(B)(C) (D) 1000C 40C 6 6 . A thermally insulated vessel contains some water at 00C. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given latent heat of vaporization of water at 0°C = 21 × 105 J/kg and latent heat of freezing of water = 3.36 × 105 J/kg. The maximum percentage amount of water that will be solidified in this manner will be:– (A) 86.2% (B) 33.6% (C) 21% (D) 24.36% 67. A closed cubical box made of perfectly insulating material has walls of thickness AB 8 cm and the only way for heat to enter or leave the box is through two solid metal E plugs A and B, each of cross–sectional area 12 cm2 and length 8 cm fixed in the opposite walls of the box as shown in the figure. Outer surface A is kept at 100°C while the outer surface B is kept at 4°C. The thermal conductivity of the material of the plugs is 0.5 cals–1cm–1 (°C–1). A source of energy generating 36 cals–1 is enclosed inside the box. The equilibrium temperature of the inner surface of the box (assuming 107
JEE-Physics that it is same at all points on the inner surface) is:– (A) 38°C (B) 57°C (C) 76°C (D) 85°C 6 8 . Three identical adiabatic containers have helium, neon and oxygen gases at the same pressure. The gases are compressed to half their original volume. Then:– (A) The final temperature of the gas in each container is same (B) The final pressure of the gas in each container is same (C) The final temperature of both helium and neon is same (D) The final pressure of both helium and neon is same 6 9 . Suppose 0.5 mole of an ideal gas undergoes an isothermal expansion as energy is added to it as heat Q. Graph shows the final volume V versus Q. The temperature of the gas is :– (use n 9 = 2 and R= 25 J/mol-K) f3 Vf(m 3)0.3 0.2 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p650.1 (A) 293 K (B) 360 K 0 500 1000 1500 (D) 412 K Q(J) (C) 386 K dN 7 0 . Graph shows a hypothetical speed distribution for a sample of N gas particle :–(for V > V ; =0) 0 dV (A) The value of V is 2N. a 0 dN (B) The ratio V /V is equal to 2/3. dV avg 0 V0 (C) The ratio V /V is equal to 1/ 2 speed V rms 0 (D) Three fourth of the total particle has a speed between 0.5 V and V . 00 71. The temperature of an isotropic cubical solid of length , density 0 and coefficient of linear expansion 0 is increased by 20°C. Then at higher temperature, to a good approximation:– (A) Length is (1+20) (B) Total sur face area is 2 (1+40) 0 0 (C) Total volume is 3 (1+60) (D) Density is 0 0 1 60 7 2 . A glass rod when measured with a zinc scale, both being at 30°C, appears to be of length 100 cm. If the scale shows correct reading at 0°C, then the true length of glass rod at 30°C and 0°C are:– (glass = 8× 10–6 °C–1, zinc = 26 × 10–6 K–1) (B) 100.078 cm, 100.078 cm (A) 100.054 cm, 100.054 cm (C) 100.078 cm, 100.054 cm (D) 100.054 cm, 100.078 cm 7 3 . Two fine steel wires, fastened between the projections of a heavy brass bar, are just taut when the whole system is at 0°C. What is the tensile stress in the steel wires when the temperature of the system is raised by 200°C? (brass = 2 × 10–5 °C–1, steel = 1.2 × 10–5 °C–1, Y = 200 GNm–2) steel (A) 3.2 Nm–2 (B) 3.2 × 108 Nm–2 (C) 32 × 108 Nm–2 (D) 0.48 Nm–2 108 E
JEE-Physics 7 4 . In a mercury–glass thermometer the cross–section of the capillary portion is A0 and the volume of the bulb is V at 273 K. If and are the coefficients of linear and cubical 0 expansion coefficients of glass and mercury respectively then length of mercury in the cap- illary at temperature t°C is (Ignore the increase in cross–sectional area of capillary) V0 3 t V0 2 3 t Capillary (A) A0 (B) A0 (C) V0 3t 273 V0 t Bulb (D) A 0 A0 7 5 . 5g of steam at 100°C is mixed with 10 g of ice at 0°C. Choose correct alternative/s) :–(Given s = 1 water cal/g°C, L = 80 cal/g, L = 540 cal/g) FV (A) Equilibrium temperature of mixture is 160°C (B) Equilibrium temperature of mixture is 1000C 12 (C) At equilibrium, mixture contain 13 g of water (D) At equilibrium, mixture contain 1 g of steam 33 7 6 . n moles of an ideal triatomic linear gas undergoes a process in which the temperature changes with volume as T = k V2 where k is a constant. Choose incorrect alternative:– 11 5 (B) At any temperature C – C = R (A) At normal temperature C = R pv v2 (C) At normal temperature molar heat capacity C=3R (D) At any temperature molar heat capacity C=3R 7 7 . A sample of gas follows process represented by PV2 = constant. Bulk modulus for this process is B, then which of the following graph is correct? BBB B (A) (B) (C) (D) PVT V 7 8 . Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture ? 16 23 19 26 (A) R (B) R (C) R (D) R 7 7 7 7 \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 7 9 . A inert gas obeys the law PVx = constant. For what value of x, it has negative molar specific heat– (A) x > 1.67 (B) x < 1.67 (C) 1 < x < 1.4 (D) 1 < x < 1.67 BRAIN TEASERS ANSWER KEY EXERCISE -2 Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 B BC C B ABCD BD Ans . B,D C C B BC BCD AB 28 29 30 31 32 33 AC B B D D ABCD D Que. 21 22 23 24 25 26 27 C D ABCD AC AC D 34 35 36 37 38 39 40 48 49 50 51 52 53 Ans . CD ABC ABD AB ABCD CD C ABBBAD D A BD B B B A Que. 41 42 43 44 45 46 47 68 69 70 71 72 73 54 55 56 57 58 59 60 CD B ABCD ACD C B Ans . B B BD D B C A C A AC D D A A Que. 61 62 63 64 65 66 67 109 74 75 76 77 78 79 Ans. A B D C A A C A BCD D ABC A D E
JEE-Physics EXERCISE–03 MISCELLANEOUS TYPE QUESTIONS TRUE / FALSE 1 . The root mean square speeds of the molecules of different ideal gases, maintained at the same temperature are the same. 2. The root mean square (rms) speed of oxygen molecules (O ) at a certain temperature T (degree absolute) is . 2 If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged. 3 . At a given temperature, the specific heat of a gas at a constant pressure is always greater than its specific heat at constant volume. 4 . Two spheres of the same material have radii 1m and 4m temperature 4000K and 2000K respectively. The energy radiated per second by the first sphere is greater than that by the second. 5 . The internal energy of a compressed gas is less than that of a rarefied gas at the same temperature. 6 . Given samples of 1 c.c. of hydrogen and 1 c.c. of oxygen, both at N.T.P. Oxygen sample has a larger molecules. 7 . A piece of metal is hammered. Its internal energy increase. 8 . Tea gets cooled, when sugar is added to it. 9 . If a bimetallic strip is heated it will bend towards the metal with higher thermal expansion coefficient. 1 0 . A bottle is filled with water at 30°C and opening at moon than water will be boil. 1 1 . The curve A and B in fig. show P–V graphs for an isothermal and an adiabatic process for an ideal gas. The isothermal process is represented by the curve A. PO A B V 1 2 . Temperature of body can be raised without heating. 1 3 . The volume V versus temperature T graphs for a certain amount of a perfect gas at two pressure P and 1 P are as shown in figure. It follows from the graphs that P is greater than P . 2 12 V P1 P2 T \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 FILL IN THE BLANKS 1 . 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 ........................... 2 . The variation of temperature of a material as heat is given to it a constant rate is shown in the figure. The material is solid state at the point O. The state of the material at the point P is................. T CD E AP B O Heat added 110
JEE-Physics 3 . The earth receives at its surface radiation from the sun at the rate of 1400 Wm–2. The distance of the centre of the sun from the surface of the ear th is 1.5 × 1011 m and the radius of the sun is 7 × 108 m. Treating the sun as a black body, it follows from the above data that its surface temperature is ......K. 4 . A solid copper sphere (density and specific heat c) of radius r at an initial temperature 200 K 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 ............. 5 . A container of volume 1 m3 is 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 .................... 6 . An ideal gas with pressure P, volume V and temperature T is expended isothermally to a volume 2V and a final pressure P . If the same gas is expanded adiabatically to a volume 2V, the final pressure is P . The ia Pa ratio of the specific heats of the gas is 1.67. The ratio Pi is ......... 7 . Two metal cubes A and B of same size are 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 and 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 ........ \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 A B 0°C T 100°C 8 . A ring shaped tube contains two ideal gases with equal masses and relative molar masses M = 32 and 1 M = 28. The gases are separated by one fixed partition and another movable stopper S which can move 2 freely without friction inside the ring. The angle as shown in the figure is ........degrees. M1 M2 S 9 . 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 × 104 N/m2. When the gas container of the same thermometer is immersed in another system, the gas pressure reads 3.5 × 104 N/m2. The temperature of this system is therefore.........°C. 1 0 . Earth receives 1400 W/m2 of solar power. If all the solar energy falling on a lens of area 0.2 m2 is focused onto a block of ice of mass 280 g, the time taken to melt the ice will be ........... minutes. (Latent heat of fusion of ice = 3.3 × 105 J/kg) 11. 2C V will be equal to ........... If the degrees of freedom of a gas are f, then CP – CV E 111
JEE-Physics Match the column 1 . Three liquids A, B and C having same specific heat and mass m, 2m and 3m have temperature 20°C, 40°C and 60°C respectively. Temperature of the mixture when : Column I Column II (A) A and B are mixed (p) 35°C (B) A and C are mixed (q) 52°C (C) B and C are mixed (r) 50°C (D) A, B and C all three are mixed (s) 45°C (t) None 2. Column–I Column–II (A) Isobaric process (p) No heat exchange (B) Isothermal process (q) Constant pressure (C) Isoentropy process (r) Constant internal energy (D) Isochoric process (s) Work done is zero 3 . Three rods of equal length of same material are joined to form an equilateral triangle ABC as shown in figure. Area of cross–section of rod AB is S, of rod BC is 2S and that of AC is S, then B A C Column II 100°C 0°C Greater than 50°C Less than 50°C Column I (p) Is equal to heat current in BC (A) Temperature of junction B (q) (B) Heat current in AB (r) 2 (C) Heat current in BC Is times heat current in AC (s) (t) 3 None 4. Column I Column II (A) In P = 2E , E is (p) Change in internal energy is only in isochoric process 3 (q) Translational kinetic energy of unit volume (B) In U=3RT for an monoatomic gas U is (r) Internal energy of one mole (s) Work done in isobaric process (C) In W = P(V – V ), W is (t) None \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 fi (D) In U = nCvT, U is V A B 5 . In the V–T graph shown in figure: T Column I Column II (A) Gas A is ... and gas B is ... (p) monoatomic, diatomic (q) diatomic, monoatomic (B) P / P is (r) > 1 AB (s) < 1 (t) cannot say any thing (C) n / n is AB 112 E
JEE-Physics 6 . For one mole of a monoatomic gas :– Column II Column I RT (A) Isothermal bulk modulus (p) V2 (B) Adiabatic bulk modulus (q) 5P (C) Slope of P–V graph in isothermal process 3V (r) T/V (D) Slope of P–V graph in adiabatic process (s) 4T/3V (t) None 7 . A copper rod (initially at room temperature 20°C) of non–uniform cross section is placed between a steam chamber at 100°C and ice–water chamber at 0°C. A and B are cross sections as shown in figure. Then match the statements in column–I with results in column–II using comparing only between cross section A and B. (The mathematical expressions in column–I have usual meaning in heat transfer). 100° 0° Steam Ice Water Chamber Chamber A B Column I Column II dQ (p) Maximum at section A (A) Initially rate of heat flow dt will be (q) Maximum at section B dQ (r) Minimum at section B (B) At steady state rate of heat flow dt will be (s) Same for all section dT (C) At steady state temperature gradient dx will be (D) At steady state rate of change of temperature dT dt at a certain point will be \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 8 . The straight lines in the figure depict the variations in temperature T as a function of the amount of heat supplied Q in different process involving the change of state of a monoatomic and a diatomic ideal gas. The initial states (P,V,T) of the two gases are the same. Match the processes as described, with the straight lines in the graph as numbered. T 1 2 3 OQ Column-II (p) 1 Column-I (q) 2 (A) Iosbaric process of monoatomic gas. (r) 3 (B) Isobaric process of diatomic gas (s) x-axis (i.e. 'Q' axis) (C) Isochoric process of monoatomic gas (D) Isochoric process of diatomic gas E 113
JEE-Physics 9. An ideal gas whose adiabatic exponent equals to 7 is expanded according to the law P=2V. The initial volume 5 25 of the gas is equal to V0= 1unit . As a result of expansion the volume increases 4 times. (Take R = 3 units) Column – I Column – II (A) Work done by the gas (p) 25 units (B) Increment in internal energy of the gas (q) 45 units (C) Heat supplied to the gas (r) 75 units (D) Molar heat capacity of the gas in the process (s) 15 units 1 0 . For a ideal monoatomic gas match the following graphs for constant mass in different processes ( = Density of gas) Column I Column II P P B B (A) A C (p) C P V A T B A (B) A C (q) C B V T T B AB (C) A C (r) C \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 T T B A C (D) A (s) C B TT 1 1 . Four rods of material X and three rods of material Y are connected as shown in figure. All the rods are of identical lengths and cross-sectional area. Given thermal resistance of rod of material X, Rx = R and thermal conductivities of materials are related by relation KY = 2KX. C AX X X Y F 100°C 0°C B X E Y Y D 114 E
JEE-Physics Column I Column II (A) Thermal resistance between B and E 500 (p) C 13 (B) Thermal resistance between A and F (q) 700 C 13 (C) Temperature of junction B 2R (r) 3 (D) Temperature of junction D 13R (s) 6 ASSERTION–REASON In each of the following questions, a Statement of Assertion (A) is given followed by a corresponding Statement of Reason (R) just below it . Of the Statements mark the correct answer as 1 . Statement–1 : A real gas behaves as an ideal gas at high temperature and low pressure. and S t atem ent –2 : Liquid state of an ideal gas is impossible. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. CP 2 . S t atem ent –1 : The ratio CV for a monatomic gas is more than for a diatomic gas. and St at eme nt –2 : The molecules of a monatomic gas have more degrees of freedom than those of a diatomic gas. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 3 . S t atem ent –1 : In adiabatic expansion of monoatomic ideal gas, if volume increases by 24% then pressure decreases by 40%. and Statem ent–2 : For adiabatic process PV = constant (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 4. S t a t e m e n t – 1 : In following figure curve (i) and (iv) represent isothermal process while (ii) & (iii) represent adiabatic process. E P (i) (ii) P (iii) (iv) P1 V P1 V P1 P1 and S t a t e m e n t – 2 : The adiabatic at any point has a steeper slope than the isothermal through the same point. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 115
JEE-Physics 5 . S t atem ent –1 : A solid material is supplied heat at a constant rate. The temp. of the material is changing with the heat input as shown in figure. Latent heat of vaporization of substance is double that of fusion (given CD = 2AB). temp E 0 CD AB 1246 and Statement–2 : Lf AB and L CD v (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 6 . S tatem ent–1 : Water kept in an open vessel will quickly evaporate on the surface of the Moon. and S tatem ent–2 : The temperature at the surface of the moon is much higher than boiling point of water at Earth. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 7 . S t a t e m e n t – 1 : Change in internal energy in the melting process is due to change in internal potential energy. and S t atem ent –2 : This is because in melting, distance between molecules increase but temperature remains constant. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 8 . S t a t e m e n t – 1 : Air quickly leaking out of a balloon becomes cooler. and Statem ent–2 : The leaking air undergoes adiabatic expansion. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 9 . Statem ent–1 : Absolute zero temperature is not the temperature of zero energy. \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 and Statem ent–2 : Only the internal kinetic energy of the molecules is represented by temperature. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 0 . S t atem ent –1 : An ideal gas has infinitely many molar specific heats. and Statem ent–2 : Specific heat is amount of heat needed to raise the temperature of 1 mole of gas by 1 K. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. E 116
JEE-Physics 1 1 . S t atem ent –1 : The bulb of one thermometer is spherical while that of the other is cylindrical. Both have equal amount of mercury. The response of the cylindrical bulb thermometer will be quicker. and S t atem ent –2 : Heat conduction in a body is directly proportional to cross–sectional area. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 2 . Statement–1 : The steam at 100°C causes more severe burn to human body than the water at 100°C. and Statem ent–2 : The steam has greater internal energy due to latent heat of vaporization. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. P (1) B 1 3 . S t atem ent –1 : A gas is taken from state A to state B through two different paths. (2) Molar specific heat capacity in path (A) is more as compared to (B). A and Statement–2 : Specific heat C QV & Q = U + W and W is equal to area under P–V diagram. nT (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 4 . St atem ent –1 : On sudden expansion a gas cools. and S t a t e m e n t – 2 : On sudden expansion, no heat is supplied to system and hence gas does work at the expense of its internal energy. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 1 5 . S t a t e m e n t – 1 : The isothermal curves intersect each other at a certain point. and S t a t e m e n t – 2 : The isothermal change are done slowly, so the isothermal curves have very little slope. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 6 . S t a t e m e n t – 1 : In a process if initial volume is equal to the final volume, work done by the gas is zero. and S t a t e m e n t – 2 : In an isochoric process work done by the gas is zero. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 7 . S t atem ent –1 : Two solid cylindrical rods of identical size and different thermal conductivity K1 and K2 are connected in series. Then the equivalent thermal conductivity of two rod system is less than the value of thermal conductivity of either rod. K1 K2 E 117
JEE-Physics and Statem ent–2 : For two cylindrical rods of identical size and different thermal conductivity K1 and K2 21 1 connected in series, the equivalent thermal conductivity K is given by K K1 K2 (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 8 . Statement–1 : When a bottle of cold carbonated drink is opened, a slight fog forms around the opening. and S t atem ent –2 : Adiabatic expansion of the gas causes lowering of temperature and condensation of water vapours. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 1 9 . S t a t e m e n t – 1 : Equal amount of heat is supplied to two identical spheres A & B (see figure). The increment in temperature for sphere A is more than sphere B. AB \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 and S t atem ent –2 : Work done due to gravity on sphere A is positive while on sphere B is negative. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 0 . S t a t e m e n t – 1 : Temperatures near the sea–coast are moderate. and Statem ent–2 : Water has a high thermal conductivity compared to ice. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 1 . S t atem ent –1 : A cloudy night is hotter than a clear sky night. and Statement–2 : Clouds are bad absorbers of heat. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 2 . Statem ent–1 : When hot water is poured in a beaker of thick glass, the beaker cracks. and Statem ent–2 : Glass is a bad conductor of heat and outer surface of the beaker does not expand. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 118 E
JEE-Physics 2 3 . Statem ent–1 : Potential energy of water at 0°C is more than ice at 0°C. and S t a t e m e n t – 2 : Heat given to melt ice at 0°C is used up in increasing the potential energy of water molecules formed at 0°C. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 4 . S t atem ent –1 : When an electric fan is switched on in a closed room, the air of the room is cooled. and S t atem ent –2 : When fan is switched on, the speed of the air molecules will increase. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 5 . Statement–1 : Snow is better insulator than ice. and Statement–2 : Snow contain air packet and air is a bad conductor of heat. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 6 . Statement–1 : Animals curl into a ball, when they feel very cold. and Statement–2 : Animals by curling their body reduces the surface area. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 7 . Statement–1 : A sphere, a cube and a thin circular plate made of same material and of same mass are initially heated to 200°C, the plate will cool at fastest rate. and Statement–2 : Rate of cooling = A (T4 – T04) surface area. Surface area is maximum for circular ms plate. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. \\\\node6\\E_NODE6 (E)\\Data\\2014\\Kota\\JEE-Advanced\\SMP\\Phy\\Unit No-5\\Thermal physics\\Eng\\Exercise.p65 2 8 . Statement–1 : High thermal conductivity of metals is due to presence of free electrons. and Statement–2 : Electrons at same temperature have very high average velocity than atoms. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. 2 9 . Statement–1 : Liquids usually expand more than solids. and Statement–2 : The intermolecular forces in liquids are weaker than in solids. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–1 (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–1 (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True. E 119
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