We provide work, energy and power practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on work, energy and power skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of work, energy and power Questions

Question No | Questions | Class |
---|---|---|

1 | A block of mass ( m ) is connected to a spring of force constant ( k . ) Initially the block is at rest and the spring has natural length. A constant force ( boldsymbol{F} ) is applied horizontally towards right. The maximum speed of the block will be (there is no friction between block and the surface) A ( cdot frac{F}{sqrt{2 m k}} ) B. ( frac{F}{sqrt{m k}} ) c. ( frac{sqrt{2} F}{sqrt{m k}} ) D. ( frac{2 F}{sqrt{m k}} ) | 11 |

2 | A body rolling down a hill has: A. K.E. only B. P.E. only C. neither K.E. nor P.E. D. both K.E. and P.E | 11 |

3 | 42. If the total mechanical energy of the particle is -40 J, then it can be found in region a. x 15 b. -10<x<-5 and 6 <x< 15 c. 10<x< 15 d. It is not possible. | 11 |

4 | 12. A system consists of two identical cubes, each of mass 3 kg, linked together by a compressed weightless spring of force constant 1000 Nm. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression xo (in cm) of the spring will the lower cube bounce up after the thread is burnt through? 3 kg &k=1000 Nm 3 kg Fig. 8.306 | 11 |

5 | A bullet of mass ( 20 mathrm{g} ) travelling horizontally with a speed of ( 500 mathrm{m} / mathrm{s} ) passes through a wooden block of mass 10.0kg initially at rest on a surface. The bullet emerges with a speed of ( 100 mathrm{m} / mathrm{s} ) and the block slides ( 20 mathrm{cm} ) on the surface before coming to rest, the coefficient of friction between the block and the surface. ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) A . 0.16 B. 0.8 c. 0.32 D. 0.24 | 11 |

6 | Read the assertion and reason carefully to mark the correct option out of the options given below: Assertion: An astronaut in a satellite | 11 |

7 | A solid cylinder of mass 2 Kg and radius ( 0.2 mathrm{m} ) is rotating about its own axis without friction with angular velocity 3 rad/s. A particle of mass 0.5 Kg and moving with a velocity of ( 5 mathrm{m} / mathrm{s} ) strikes the cylinder and sticks to it as shown in. The angular momentum of the cylinder before collision will be A. 0.12 Joule/s B. 12 Joule/s c. 1.2 Joule/s D. 1.12 Joule/s | 11 |

8 | The angular momentum of an electron in the hydrogen atom is ( frac{3 h}{2 pi} ). Here h is Planck’s constant. The kinetic energy of this electron is: A . 4.53 ev B. 1.51 eV c. 3.4 ev D. 6.8 ev | 11 |

9 | Illustration 8.59 An elevator of mass M with a per mass m is moving upward with uniform velocity v. What is the power delivered by the elevator? Fig. 8.161 | 11 |

10 | When the bob of a simple pendulum swings, the work done by tension in the string is? ( mathbf{A} cdot>0 ) B . ( <0 ) c. zero D. maximum | 11 |

11 | Calculate the forces ( F(y) ) associated with the following one-dimensional potential energies: (a) ( U=-omega y ) (b) ( U=a y^{3}-b y^{2} ) ( (c) U=U_{0} sin beta gamma ) | 11 |

12 | The block of mass ( M ) moving on the frictionless horizontal surface collides with the spring of spring constant ( boldsymbol{K} ) and compresses it by length ( L ). The maximum moment of the block after collision is A ( cdot sqrt{M K} L ) в. ( frac{K L^{2}}{2 M} ) c. zero D. ( frac{M L^{2}}{K} ) | 11 |

13 | Force constants of two wires ( A ) and ( B ) of the same material are ( K ) and ( 2 K ) respectively. If two wires are stretched equally, then the ratio of work done in stretching ( left(frac{W_{A}}{W_{B}}right) ) is: A ( cdot frac{1}{2} ) B. ( frac{3}{2} ) ( c cdot frac{1}{4} ) D. | 11 |

14 | determine the total work done on the block A . 12.45 B . 24.9 c. 49.8 D. 99.6 | 11 |

15 | On a friction less surface, a ball of mass ( m ) moving at a speed ( v ) makes a headon collision with an identical ball at rest. The kinetic energy of the balls after the collision is ( frac{3}{4} t h ) of the original. Find the coefficient of restitution? A ( frac{1}{sqrt{2}} ) в. ( frac{1}{sqrt{3}} ) c. ( frac{3}{sqrt{2}} ) D. ( frac{1}{sqrt{5}} ) | 11 |

16 | A particle falls from a height ‘ ( h^{prime} ) upon a fixed horizontal plane and rebounds. If ( e^{prime} ) is the coefficient of restitution, the total distance travelled before it comes to rest is ( ^{text {A }} ). ( hleft(frac{1+e^{2}}{1-e^{2}}right) ) B ( quad hleft(frac{1-e^{2}}{1+e^{2}}right) ) c. ( frac{H}{2}left(frac{1-e^{2}}{1+e^{2}}right) ) D. ( frac{H}{2}left(frac{1+e^{2}}{1-e^{2}}right) ) | 11 |

17 | The displacement of ( m^{prime} ) on ( M ) is A ( .0 .3 m ) в. ( 0.2 m ) c. ( 0.98 m ) D. ( 0.1 m ) | 11 |

18 | A ball collides with a smooth and fixed inclined plane of inclination ( boldsymbol{theta} ) after falling vertically through a distance h. If it moves horizontally just after impact, the coefficient of restitution is ( mathbf{A} cdot tan ^{2} theta ) B ( cdot cot ^{2} theta ) ( c . tan theta ) D. ( cot theta ) | 11 |

19 | Impulse of force is A. Product of average force and time B. Division of average force and time C. Integration of average force and time D. All of the above | 11 |

20 | The potential energy of a rocket of mass ( 100 k g ) at height ( 10^{7} m ) from earth surface is ( 4 times 10^{9} ) Joule. The weight of the rocket at height ( 10^{9} ) will be ( mathbf{A} cdot 4 times 10^{-2} N ) В . ( 4 times 10^{-3} N ) c. ( 8 times 10^{-2} N ) D. ( 8 times 10^{-3} N ) | 11 |

21 | Moon is a satellite of the Earth, but weightlessness is not experienced at the surface of the Moon because A. its distance from the Earth is more B. it is a natural satellite c. its size is big but density is very low. D. its own mass is more | 11 |

22 | A constant horizontal ( 4.0 N ) force acts on a ( 300 g ) cart on a horizontal track as the cart moves through a distance of ( 43.0 mathrm{cm} . ) The cart decelerates as a result. What was the work performed on the cart by the force? в. ( -1.27 J ) c. ( 1.27 J ) D. ( 1.72 J ) E. None of the above | 11 |

23 | Find the angle between ( vec{a}+vec{b}+vec{c} ) and ( vec{a}+vec{b}-vec{c} ) A ( cdot cos ^{-1}left(frac{8}{sqrt{57}}right) ) B. ( cos ^{-1}left(frac{9}{sqrt{75}}right) ) ( ^{mathbf{C}} cdot cos ^{-1}left(frac{1}{sqrt{2}}right) ) D. ( cos ^{-1}left(frac{-7}{sqrt{85}}right) ) | 11 |

24 | Work done by the gravitational force on a body of mass ( m ) moving on a smooth horizontal surface through a distance is: (Given acceleration due to gravity = ( boldsymbol{g}) ) A . ( m g s ) B. ( -m g s ) c. 0 D. ( 2 m g s ) | 11 |

25 | Two particles of mass ( m_{1} ) and ( m_{2} ) in projectile motion have velocities ( vec{v}_{1}< ) ( vec{v}_{2} ) respectively at tine ( t=0 . ) They collide at time ( t_{0} . ) Their velocities become ( overrightarrow{v_{1}^{prime}} ) and ( vec{v}_{2}^{prime} ) at time ( 2 t_{0^{prime}} ) while still moving in air. The value of ( left|left(m_{1} vec{v}_{1}^{prime}+m_{2} overrightarrow{v_{2}^{prime}}right)-left(m_{1} vec{v}_{1}+m_{2} vec{v}_{2}right)right| ) | 11 |

26 | A trolley is under the action of a constant force ( F ). The sand contained by it is poured out through a hole in the floor at the rate of ( m ) per second.lf initial mass of sand and trolley was ( M ) and initial speed was ( u, ) the acceleration of trolley at time ( t ) is given by ( A ) в. c. ( frac{F}{M-m} ) D. ( frac{F}{M+m} ) | 11 |

27 | Identify the wrong statement. A. ( A ) body can have momentum without energy B. A body can have energy without momentum. C. The momentum can conserved in an elastic collision. D. Kinetic energy is not conserved in an inelastic collision | 11 |

28 | What is the angle between two vector forces of equal magnitude such that their resultant is one-third of either of the original forces? ( ^{mathbf{A}} cdot cos ^{-1}left(-frac{17}{18}right) ) B. ( cos ^{-1}left(-frac{1}{3}right) ) ( c cdot 45^{circ} ) D. ( 120^{circ} ) | 11 |

29 | A car is being driven at a constant speed of ( 5 m / s ) by a force of ( 3 times 10^{8} N ) It takes 2 minutes to reach its destination. What is the work done? A ( .15 times 10^{8} J ) B . ( 18 times 10^{10} J ) c. ( 6 times 10^{10} J ) D . ( 10 times 10^{8} J ) | 11 |

30 | 30. The system shown in Fig. 8.232 is released from rest with mass 2 kg in contact with the ground, Pulley and spring are massless, and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with the ground is (force constant of the spring k 40 Nm and 8 = 10 ms?) 5 kg 12 kg a. 2 ms- c. 2 ms! Fig. 8.232 b. 2/2 ms. d. 2 ms’ atende on weighing balance working | 11 |

31 | It is well known that a raindrop or a small pebble falls under the influence of the downward gravitational force and the opposing resistive force. The resistive force is known to be proportional to the speed of the drop. Consider a drop or small pebble of 1 g falling (from rest) from a diff of height ( 1.00 mathrm{km} . ) It hits the ground with a speed of ( 50.0 mathrm{m} s^{-1} . ) What is the work done by the unknown resistive force? | 11 |

32 | A metal ball falls from a height 1 m on a steel plate and jumps up to a height of ( 0.81 m . ) Find the coefficient of restitution | 11 |

33 | A block of mass ( m=0.1 mathrm{kg} ) is released from a height of ( 4 mathrm{m} ) on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC offers coefficient of friction ( mu=0.1 . ) If the impact of block with the vertical wall at C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be : ( left(operatorname{take} g=10 m / s^{2}right) ) A. ( 29 mathrm{m} ) B. 49 ( mathrm{m} ) c. ( 59 mathrm{m} ) D. ( 109 mathrm{m} ) | 11 |

34 | A sphere of mass ( m ) moving with constant velocity hits another sphere of same mass at rest. If ( e ) is the coefficient of restitution. The ratio of their velocities after collision is : ( mathbf{A} cdot 1+e ) B. ( frac{1+e}{2} ) ( c cdot frac{1+2 e}{1-2 e} ) D. ( frac{1-e}{1+e} ) | 11 |

35 | A uniform chain of length ( pi r ) lies inside a smooth semicircular tube ( A B ) of radius ( r . ) Assuming a slightly disturbance to start the chain in motion, the velocity with which it will emerge from the end ( mathrm{B} ) of tube will be: ( sqrt[A cdot]{g rleft(1+frac{2}{pi}right)} ) B. ( sqrt{2 g rleft(frac{2}{pi}+frac{pi}{2}right)} ) c. ( sqrt{g r(pi+2)} ) D. ( sqrt{pi g r} ) | 11 |

36 | ( mathbf{A} ) 300 pound fullback carrying the football towards the goal line encounters a 150 pound defensive back near the goal line. The two are moving at the same speed when they both leave their feet and collide head-on in mid-air. The defensive back goes flying backward, and the fullback continues forward, scoring a touchdown. As a result of the collision. How do the player’s changes in momentum compare? A. The amount of the defensive back’s momentum changes is twice as much as the fullback’s B. The amount of the fullback’s momentum changes is twice as much as the back’s c. The amount of the defensive back’s momentum changes is more than twice as much as the fullback’s D. The amount of the fullback’s momentum change is more than twice as much as the fullback’s E. The amount of momentum change for each player is the same | 11 |

37 | Two balls shown in figure are identical Ball ( A ) is moving towards right with a speed ( v ) and the second ball is at rest. Assume all collisions to be elastic. Show that the speed of the balls remain unchanged after all the collisions have takes place (Assume frictionless surface) | 11 |

38 | What is the gravitational potential energy of the mass ( m ? ) ( ^{mathbf{A}} cdot frac{2}{sqrt{3}} frac{G M m}{l}(1-2 sqrt{3}) ) B. ( -frac{2}{sqrt{3}} frac{G M m}{l}(1+2 sqrt{3}) ) ( ^{mathbf{c}}-frac{sqrt{3}}{2} frac{G M m}{l}(1-2 sqrt{3}) ) D. ( -frac{sqrt{3}}{2} frac{G M m}{l}(1+2 sqrt{3}) ) | 11 |

39 | If ( g ) is acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( m ) raised from the surface of the earth to a height equal to the radius ( R ) of the earth is: A. ( 2 m g R ) в. ( m g R ) c. ( frac{m g R}{4} ) D. ( frac{m g R}{2} ) | 11 |

40 | Energy stored in a stretched spring is gravitational potential energy. A. True B. False c. Ambiguous D. Data insufficient | 11 |

41 | Assertion In an elastic collision of two bodies, the momentum and energy of the system are conserved. Reason If two bodies stick to each other, after colliding, the collision is said to be perfectly inelastic. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

42 | 17. The velocity-time graph of a particle moving in a straight line is shown in Fig. 8.227. The mass of the particle is 2 kg. Work done by all the forces acting on the particle in time interval between t=0 to t = 10 s is v(ms) 10 10 Fig. 8.227 b. -300 J C. 400 J a. 300 J d. – 400 J A .. . .1 | 11 |

43 | Assertion Displacement ( (S) ) -time (t) graph of a particle moving in a straight line is shown in figure. Work done by all the forces is equal to change in kinetic energy. Reason Work done by all the forces between time interval ( t_{1} ) and ( t_{2} ) is definitely zero. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion. C. Assertion is correct but Reason is incorrect. D. Both Assertion and Reason are incorrect. | 11 |

44 | A massive ball moving with speed ( mathbf{v} ) collides head-on with a tiny ball at rest having a very small mass as compared to the first ball. If the collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to ( A ) B. 2v ( c cdot v / 2 ) D. ( infty ) | 11 |

45 | Find total work done on the block as it moves by ( 4 m ) as shown | 11 |

46 | Illustration 8.19 A smooth block of mass m moves up from bottom to top of a wedge which is moving with an acceleration ao. Find the work done by the pseudo force measured by the person sitting at the edge of the wedge. Fig. 8.42 | 11 |

47 | frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from ( 60^{circ} ) and ( 30^{circ} ) at point ( B ) The block is initially at rest at ( boldsymbol{A} ) Assume that collisions between the block and the incline are totally inelastic. The speed of the block at point ( B ) immediately after it strikes the second incline is ( mathbf{A} cdot sqrt{60} m / s ) B. ( sqrt{45} mathrm{m} / mathrm{s} ) ( mathbf{c} cdot sqrt{30} m / s ) D. ( sqrt{15} mathrm{m} / mathrm{s} ) | 11 |

48 | A body is lifted over route I and then route II such that force is always tangent to the path. Coefficient of friction is same for both the paths. Work done A. on both routes is same B. on route lis more c. on route II is more. D. on both routes is zero | 11 |

49 | A ball collides elastically with another ball of the same mass. The collision is oblique and initially one of the ball was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocity of the balls after the collision? A ( .30^{circ} ) B . 45 ( c cdot 60 ) D. 90 | 11 |

50 | A bullet mass ( m ) is fired at a certain angle q with the vertical. The bullet is returned to ground in time. The total change of momentum is equal to then : ( A cdot m g / 2 ) B. mgt c. ( 2 mathrm{mgt} ) D. mg | 11 |

51 | A particle moves along the ( x ) -axis from ( x=0 ) to ( x=5 m ) under the influence of a force given by ( boldsymbol{F}=mathbf{7}-mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{x}^{2} boldsymbol{N} ) The work done in the process is ( mathbf{A} cdot 107 J ) B. ( 270 J ) c. ( 100 J ) D. ( 135 J ) | 11 |

52 | Work done by kinetic friction on a body is never zero. A. True B. False c. Ambiguous D. Data insufficient | 11 |

53 | Find the speed of A after all collisions end. A ( cdot frac{V}{8} ) B. ( frac{V}{4} ) c. ( frac{3 V}{8} ) D. ( 2 V ) | 11 |

54 | Illustration 8.10 A block of mass 5 kg is being raised vertically upwards by the help of a string attached to it la rises with an acceleration of 2 ms. Find the work done hu the tension in the string if the block rises by 2.5 m. Also find the work done by the gravity and the net work done. | 11 |

55 | During one dimensional collision or head on collision: a) The bodies move along the line joining their centre of mass before and after collision. b) The bodies should move in opposite direction. c) The bodies change their direction after collision. d) The bodies move along the line joining their centre of mass before and after collision either in same direction or in opposite direction. A. Only a is correct B. Only a & b are correct ( c . ) a, b ( & mathrm{c} ) are correct D. Only a and d are correct | 11 |

56 | A uniform cylinder of radius ( r ) and length L and mass ( m ) is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is: ( ^{mathbf{A}} cdot_{m g}left[left(frac{L}{2}right)-rright] ) ( ^{mathrm{B}}_{m g}left[left(frac{g}{2}right)-rright] ) c. ( m(g L-1) ) D. ( M g L r ) | 11 |

57 | An inelastic ball is dropped from a height of ( 100 mathrm{cm} . ) Due to collision with the earth ( 20 % ) of its energy is lost. To what height will the ball rise? ( mathbf{A} cdot 80 mathrm{cm} ) B. ( 40 mathrm{cm} ) c. ( 60 mathrm{cm} ) D. ( 20 mathrm{cm} ) | 11 |

58 | Two vectors of equal magnitude have a resultant equal to either of them. Then, the angle between them will be ( 2 pi / 3 ) radians. The angle in degrees is: A ( .30^{circ} ) B. ( 120^{circ} ) ( c cdot 60 ) D. ( 45^{circ} ) | 11 |

59 | A radioactive nucleus decays by ( boldsymbol{beta} ) emission. Both ( beta ) and neutrino move mutually at right angle with momentum ( 6 times 10^{-21} k g m s^{-1} ) and ( 3 times ) ( 10^{-21} k g m s^{-1} . ) The direction of recoil of nucleus with respect to electron is : A ( cdot tan ^{-1}left(frac{1}{2}right) ) B. ( tan ^{-1}(2) ) c. ( _{180-tan ^{-1}}left(frac{1}{2}right) ) D. ( 180-tan ^{-1}(2) ) | 11 |

60 | spring. 1500 Nm, k2 = 500 Nm’,m, = 2 kg, m,= 8. Given k, = 1500 Nm 1 kg. Find: L00001 mi Leelle m2 Fig. 8.212 a. potential energy stored in the springs in equilibrium, and b. work done in slowly pulling down m, by 8 cm. mis doned onto | 11 |

61 | If a force of ( 4 N ) is applied on a body of mass ( 20 k g ), then the work done in ( 3 r d ) second will be A ( .1 .2 J ) в. ( 2 J ) c. 45 D. 16 ( J ) | 11 |

62 | Under the action of a force ( boldsymbol{F}=boldsymbol{C x} ), the position of a body changes from 0 to ( x ) The work done is : ( ^{mathbf{A}} cdot frac{1}{2} C x^{2} ) в. ( C x^{2} ) ( c cdot C x ) D. ( frac{1}{2} C x ) | 11 |

63 | A ball moving with a momentum of ( 5 k g m / s ) strikes against a wall at angle of ( 45^{circ} ) and is deflected at the same angle. Calculate the change in momentum. | 11 |

64 | A cyclist free-wheels from the top of a hill, gathers speed going down the hill, apply his brakes and eventually came to rest at the bottom of the hill. Which one of the following energy changes take place? A. Potential to kinetic to heat energy B. Kinetic to potential to heat energy c. Chemical to heat to potential energy D. Kinetic to heat to chemical energy | 11 |

65 | A bar of mass ( M ) and length ( L ) is in pure translatory motion and its centre of mass has velocity ( V ). It collides and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length ( 2 L ) ). The angular velocity of the composite bar after collision will be : This question has multiple correct options A ( cdot frac{3}{4} frac{V}{L} ) в. ( frac{4}{3} frac{V}{L} ) c. counterclockwise D. Clockwise | 11 |

66 | A ball after falling a distance of 5 meter from rest hits floor of a lift and rebounds. At the time of impact the lift was moving up with a velocity of 1 ( m / ) sec. The velocity with which the ball rebounds just after impact is- ( (g= ) ( mathbf{1 0} boldsymbol{m} / boldsymbol{s e c}^{2} ) A. ( 10 mathrm{m} / mathrm{sec} ) B. ( 11 mathrm{m} / mathrm{sec} ) c. ( 12 mathrm{m} / mathrm{sec} ) D. ( 13 mathrm{m} / mathrm{sec} ) | 11 |

67 | Three forces ( (hat{i}+3 hat{j}+hat{k}), frac{5}{7}(-2 hat{i}+9 hat{k}) ) and ( 11(2 hat{i}+hat{j}+6 hat{k}) ) are acting on a particle. Calculate the work done in displacing the particle from point (4,-1,1) to point (11,6,8) | 11 |

68 | A body of mass ( 0.1 mathrm{kg} ) is dropped from a height of ( 10 mathrm{m} ) at a place wheres ( g= ) ( 10 m s^{-2} . ) Its KE just before its strikes the ground is: A . 1 B. 1.04 J c. 3.5 D. 10J | 11 |

69 | A man weighing ( 60 mathrm{kg} ) lifts a body of mass 15 kg to the top of a building 10 m high in 3 minutes. His efficiency is A . ( 20 % ) B. ( 10 % ) ( c .30 % ) D. ( 40 % ) | 11 |

70 | 19. A car drives along a straight level frictionless road by an engine delivering constant power. Then velocity is directly proportional to a. t b. c. Se d. None of these | 11 |

71 | State and explain work energy principle. Mention any three examples for it. | 11 |

72 | Find the ratio ( m_{1}: m_{2} ? ) ( A ) B. ( sqrt{2} ) c. ( 1 / sqrt{2} ) D. 2 | 11 |

73 | A ball is dropped from height hon the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is : A ( cdot frac{h}{e^{2 n}} ) B. ( frac{e^{2 n}}{h} ) ( c cdot h e^{2 n} ) D. ( h e^{n} ) | 11 |

74 | 28. Work done by friction on the boy is a. Equal to work done by boy b. Equal to work done by the motor in running the conveyor belt c. Zero d. None of above | 11 |

75 | In which of the following cases is the work done positive or zero or negative? a) Work done by the porter on a suitcase in lifting it from the platform on to his head. b) Work done by the force of gravity on suitcase as the suitcase falls from porter’s head. c) Work done by the porter standing on platform with suitcase on his head. d) Work done by force of gravity on a ball thrown up vertically up into the sky. e) Work done by force applied by hands of a man swimming in a pond. | 11 |

76 | The potential energy of a particle of mass ( 0.5 mathrm{kg} ) moving along ( mathrm{x} ) -axis is given by ( U=left(x^{2}-4 xright) ) joule where ( x ) is in metres. The time period of oscillation of the particle is? | 11 |

77 | A bomb of ( 12 mathrm{kg} ) explodes into two pieces of masses 4 kg and 8 kg. The velocity of ( 8 mathrm{kg} ) mass is ( 6 mathrm{m} ) per second .The kinetic energy of other mass is? A. 48 joules B. 32 joules c. 24 joules D. 288 joule | 11 |

78 | A block of mass ( 5.0 mathrm{kg} ) slides down an incline of inclination ( 30^{0} ) and length 10 m. Find the work done by the force of gravity in joules? A . 245 B. 300 ( c .350 ) D. 400 | 11 |

79 | A box is put on a scale which is adjusted to read zero,when the box is empty. A stream of pebbles is then poured into the box from a height ( h ) above its bottom at a rate of n pebbles collide with the box such that they immediately come to rest after collision, the scale reading at time ( t ) after the pebbles begin to fill the box is: ( mathbf{A} cdot m n{sqrt{(2 g h)}+g t} ) B. ( {sqrt{(2 g h)+g t}} ) c. ( {sqrt{(2 g h)-g t}} ) D ( cdot operatorname{mn}{(2 g h)-g t} ) | 11 |

80 | Which statement best represents the principle of conservation of energy? A. Energy cannot be used faster than it is created. B. The supply of energy is limited, so energy must be conserved C. The total energy in a closed system is constant D. The total energy input to a system is equal to the useful energy output | 11 |

81 | If ( |vec{A}|=|vec{B}|, ) then what is the angle between ( vec{A}+vec{B} ) and ( vec{A}-vec{B} ) A ( cdot 90^{circ} ) B. 60 ( c .30 ) D. 0 | 11 |

82 | A bread gives a boy of mass ( 40 k g ) an energy of ( 21 k J . ) If the efficiency is ( 28 % ) then the height can be climbed by him using this energy is ( mathbf{A} cdot 22 cdot 5 m ) в. ( 14.7 m ) ( c .5 m ) D. ( 10 m ) | 11 |

83 | a) How are work, force and distance related. b) Find the work done by a pulley when it lifts a block which is 5 m off the ground with a ( 10 mathrm{N} ) force. | 11 |

84 | A force ( boldsymbol{F}=-boldsymbol{K}(boldsymbol{y} hat{boldsymbol{i}}-boldsymbol{x} hat{boldsymbol{j}}), ) (where ( boldsymbol{K} ) is a positive constant) acts on a particle moving in the ( X Y ) -plane. Starting from the origin, the particle is taken along the positive ( X ) -axis to the plane ( (a, 0) ) and then parallel to the ( Y ) -axis to the point ( (a, a) . ) The total work done by the force ( F ) on the particle is A ( .-2 K a^{2} ) B ( .2 K a^{2} ) c. ( -K a^{2} ) D. ( K a^{2} ) | 11 |

85 | A particle is moved from (0,0) to ( (a, a) ) under a force ( F=3 i+4 j ) ) from two paths. Path 1 is ( 0 P ) and path 2 is ( Q O P ). Let ( W_{1} ) and ( mathrm{W}_{2} ) be the work done by this force in two paths. Then: A. ( w_{1}=w_{2} ) B. ( w_{1}=2 w_{2} ) ( c cdot w_{2}=2 w_{1} ) ( D cdot W_{1}=4 W_{2} ) | 11 |

86 | A particle is projected at time ( t=0 ) from a point ‘O’ with a speed ‘u’ at an angle ‘ ( theta ) to horizontal. Find the torque of a gravitational force on projectile about the origin at time ‘t’. (x, y plane is vertical plane) | 11 |

87 | The coefficient of restitution of a perfectly elastic collision is : A . B. 0 ( c cdot infty ) D. – | 11 |

88 | In a one-dimensional elastic collision, the relative velocity of approach before collision is equal to: A. sum of the velocities of the bodies B. ( e ) times the relative velocity of separation after collision c. ( 1 / e ) times the relative velocity of separation after collision D. relative velocity of separation after collision | 11 |

89 | The net work done by the tension in the figure when the bigger block of mass ( M ) touches the ground is: ( mathbf{A} cdot+M g d ) в. ( -(M+m) g d ) ( mathrm{c} .-m g d ) D. zer | 11 |

90 | ( mathbf{A} ) ( 3 k g ) object has initial velocity ( (6 hat{i}- ) ( mathbf{2} hat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} . ) The total work done on the object if its velocity changes to ( (8 hat{i}+ ) ( 4 hat{j}) m / s ) is : A .2165 J 52665.53 в. ( 44 J ) c. ( 60 J ) D. ( 120 J ) | 11 |

91 | Illustration 8.7 A chain of length L and mass M is held on a frictionless table with (1/n)th of its length hanging over the edge (Fig. 8.9). Calculate the work done in pulling the chain slowly on the table against gravity. Fig. 8.9 | 11 |

92 | A ladder ( ^{prime} A B^{prime} ) of weight ( 300 N ) and length ( 5 m ) is lying on a horizontal surface. Its centre of gravity is at a distance of ( 2 m ) from end ( A . ) A weight of ( 80 N ) is attached at end ( B ). The work done in raising the ladder to the vertical position with end ( ^{prime} boldsymbol{A}^{prime} ) in contact with the ground is. A. ( 500 J ) в. ( 1000 J ) c. ( 1150 J ) D. ( 1900 J ) | 11 |

93 | Which of the following devices convert light energy into electrical energy? A. An electric bulb B. A photocell c. A microphone D. A dynamo | 11 |

94 | A block of mass ( 10 k g ) is released on a fixed wedge inside a cart which is moved with constant velocity ( 10 mathrm{ms}^{-1} ) towards right. There is no relative motion between block and cart. Then work done by normal reaction on block in two seconds from ground frame will be ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) ) A . ( 1320 J ) В. ( 960 J ) c. ( 1200 J ) D. ( 240 J ) | 11 |

95 | A body of mass 5 kg moving with a speed of ( 3 m s^{-1} ) collides head on with a body of mass ( 3 mathrm{kg} ) moving in the opposite direction at a speed of ( 2 m s^{-1} ) The first body stops after the collision. Find the final velocity of the second body. ( mathbf{A} cdot 3 m s^{-1} ) B . ( 5 mathrm{ms}^{-1} ) ( mathrm{c} cdot-9 mathrm{ms}^{-1} ) D. ( 30 m s^{-1} ) | 11 |

96 | 58. In the above question, the maximum power delivered by the agent in pulling up the rope is a. I lgv b. a ON c. Mgv + v32 X | 11 |

97 | Assertion Work-energy theorem can be applied for non-inertial frames also. Reason Earth is a non-inertial frame. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

98 | If the potential energy between electron and proton at a distance ( r ) is given by ( U=-left(frac{k e^{2}}{3 r^{3}}right) . ) The force is : A ( cdot_{F}=frac{k e^{2}}{r^{2}} ) B. ( _{F}=-frac{3}{4} frac{k e^{2}}{r^{4}} ) ( ^{mathrm{c}} cdot_{F}=frac{k e^{2}}{r^{4}} ) D. ( _{F}=frac{k e^{2}}{r} ) | 11 |

99 | As per given figure to complete the circular loop what should be the radius if initial is ( 5 m ) A . ( 4 m ) B. 3 m c. ( 2.5 m ) D. ( 2 m ) | 11 |

100 | A vector ( vec{A}=2 hat{i}+3 hat{j}+6 hat{k} ) makes an angle of ( beta ) with positive direction of ( x- ) axis. ( beta ) is equal to: A ( cdot tan ^{-1} frac{2}{7} ) B. ( sin ^{-1} frac{2}{7} ) ( c cdot cos ^{-1} frac{2}{7} ) D. ( cos ^{-1} frac{4}{7} ) | 11 |

101 | A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be: ( ^{A} cdotleft(frac{1-e}{1+e}right) ) в. ( left(frac{1+e}{1-e}right) ) c. ( left(frac{e+1}{e-1}right) ) D. ( left(frac{e-1}{e+1}right) ) | 11 |

102 | Given: ( overrightarrow{boldsymbol{A}}=boldsymbol{i}-mathbf{2} boldsymbol{j}, overrightarrow{boldsymbol{B}}=mathbf{2} hat{mathbf{i}}+ ) ( mathbf{3} hat{boldsymbol{k}} boldsymbol{a} boldsymbol{n} boldsymbol{d} overrightarrow{boldsymbol{C}}=hat{boldsymbol{i}}+hat{boldsymbol{j}} ) Find component of vector ( overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}} ) along: (i) x-axis (ii) ( overrightarrow{boldsymbol{C}} ) A ( cdot 3 ; frac{1}{sqrt{2}} ) в. ( 2 ; frac{1}{sqrt{3}} ) c. ( _{3 ; frac{1}{sqrt{3}}} ) D. ( 2 ; frac{1}{sqrt{2}} ) | 11 |

103 | From a rifle of mass ( 4 k g, ) a bullet of mass ( 50 g ) is fired with an initial velocity of ( 35 m s^{-1} ). Calculate the initia recoil velocity of the rifle. | 11 |

104 | In a collinear collision, a particular with an initial speed ( v_{0} ) strikes a stationary particle of the same mass. If the final total kinetic energy is ( 50 % ) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is? ( A cdot frac{v_{0}}{2} ) в. ( frac{v_{0}}{sqrt{2}} ) c. ( frac{v_{0}}{4} ) ( D cdot sqrt{2} v_{0} ) | 11 |

105 | 1. When the cord is burnt with a match releasing the spring. the two masses fly apart with equal a. Kinetic energy b. Speed c. Momentum d. Acceleration WL: 1viro2 | 11 |

106 | A girl weighing 50 kg makes a high jump of ( 1.2 mathrm{m} . mathrm{What} ) is her kinetic energy at the highest point? ( left(boldsymbol{g}=mathbf{1 0 m s}^{-mathbf{2}}right) ) A. 6000 B. 600 J c. 60 J D. zero | 11 |

107 | A point mass ( M ) moving with a certain velocity collides with a stationary point mass ( frac{M}{2} . ) The collision is elastic and one dimension. Let the ratio of the final velocities of ( M ) and ( frac{M}{2} ) be ( x ). The value of ( x ) is : ( A cdot 2 ) B. 3 ( c cdot frac{1}{2} ) D. | 11 |

108 | Q Type your question- the figure. The coefficient of friction, between the particle and the rough track equals ( mu . ) The particle is released, from rest, from the point ( boldsymbol{P} ) and it comes to rest at a point ( R ). The energies, lost by the ball, over the parts, ( P Q ) and ( Q R ), of the track, are equal to each other, and no energy is lost when particle changes direction from ( P Q ) to ( Q R ) The values of the coefficient of friction ( mu ) and the distance ( x(=Q R), ) are respectively close to. A. 0.2 and 6.5 m B. 0.2 and 3.5 m c. 0.29 and ( 3.5 m ) D. 0.29 and 6.5 | 11 |

109 | A force ( boldsymbol{F}=(mathbf{1 0}+mathbf{0 . 5} boldsymbol{x}) boldsymbol{N} ) acts on a particle in ( X ) direction, where ( x ) is in meters. Find the work done by this force during a displacement from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{2} ) | 11 |

110 | A ball is dropped on the ground from the height of ( 1 m . ) The coefficient of restitution is ( 0.6 . ) The height to which the ball will rebound is (in ( m) ) A . 0.6 B. 0.4 ( c .0 .36 ) D. 0.16 | 11 |

111 | If ( A+B=C ) and that ( C ) is perpendicular to ( A ). What is the angle between ( boldsymbol{A} ) and ( boldsymbol{B} ), if ( |boldsymbol{A}|=|boldsymbol{C}| ) ? A ( cdot frac{pi}{4} r a d ) B. ( frac{pi}{2} r a d ) c. ( frac{3 pi}{4} r a d ) D. ( pi r a d ) | 11 |

112 | Two masses ( m_{1}=10 mathrm{kg} ) and ( m_{2}= ) ( 5 k g ) are connected by an ideal string as shown in the figure. The coefficient of friction between ( m_{1} ) and the surface is ( mu=0.2 . ) Assuming that the system is released from rest. The velocity of blocks when ( m_{2} ) has descended by ( 4 m ) is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) ) A. ( 4 mathrm{m} / mathrm{s} ) в. ( 8 mathrm{m} / mathrm{s} ) c. ( 2 m / s ) D. ( 12 mathrm{m} / mathrm{s} ) | 11 |

113 | Two particles of equal mass go around a circle of radius ( R ) under the action of their mutual gravitational attraction. The speech of each particle is ( ^{mathbf{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G M}right)} ) в. ( v=sqrt{left(frac{G M}{2 R}right)} ) ( ^{mathrm{c}} cdot_{v}=frac{1}{2} sqrt{left(frac{G M}{R}right)} ) D. ( v=sqrt{left(frac{4 G M}{R}right)} ) | 11 |

114 | A body of mass ( m ) starts moving with velocity ( V_{0} ) at point ( A ) on a frictionless path as shown in the figure. The speed of the body at point ( B ) will be: | 11 |

115 | When two bodies collide, they each other. A. Push B. Pull c. Moves towards D. All | 11 |

116 | A tennis ball has a mass of ( 56.7 g m ) and is served by a player with a speed of 180kmph. The work done in serving the ball is nearly: begin{tabular}{l} A. 7105 \ hline end{tabular} в. ( 71 J ) ( mathrm{c} .918 mathrm{J} ) D. ( 91.8 J ) | 11 |

117 | A boy of mass ( M ) stands on a platform of radius ( R ) capable to rotate freely about its axis. The moment of inertia of the platform is ( I . ) The system is at rest. The friend of the boy throws a ball of mass ( m ) with a velocity ( v ) horizontally. The boy on the platform catches it. Find the angular velocity of the system in the process. A ( cdot frac{m v R}{(M+m) R^{2}} ) в. ( frac{m v}{I+M R^{2}} ) c. ( frac{m v R}{I+m R^{2}} ) D. ( frac{m v R}{I+(M+m) R^{2}} ) | 11 |

118 | A mass ( m_{1} ) moves with a great velocity. It strikes another mass ( m_{2} ) at rest in a head on collision and comes back along its path with a low speed after collision. Then : ( mathbf{A} cdot m_{1}>m_{2} ) В. ( m_{1}=m_{2} ) ( mathbf{c} cdot m_{1}<m_{2} ) D. there is relation between ( m_{1} ) and ( m_{2} ) | 11 |

119 | Illustration 8.62 A small body of mass m is located on a horizontal plane at the point O. The body acquires a horizontal velocity Vo. Find the mean power developed by the friction force during the whole time of motion, if the frictional coefficient u = 0.27, m= 1.0 kg and yo = 1.5 ms-1. SO | 11 |

120 | The mass of a bucket containing water is ( M_{0} . ) The bucket is pulled steadily up from a well of depth d. Due to a hole in the bucket the water is pouring out at a uniform rate and as a result the mass of the bucket with water at the top of the well reduces to M. Then the amount of work done in pulling up the bucket is? A ( cdotleft(M_{0}-Mright) g d ) в. ( frac{1}{2}left(M_{0}-Mright) g d ) c. ( left(M_{0}+Mright) g d ) D. ( frac{1}{2}left(M_{0}+Mright) g d ) | 11 |

121 | It is observed that for a ratio ( frac{boldsymbol{m}_{1}}{boldsymbol{m}_{2}}= ) ( left(3-x^{2}+xright), ) maximum transfer of momentum takes places from body 1 to body ( 2 . ) Then This question has multiple correct options A ( . x=1 ) B. ( x=2 ) ( c cdot x=3 ) D. x = – | 11 |

122 | A sphere of mass ( m ) moving with velocity ( v ) hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in terms of ( e ) ) A ( cdot frac{v_{1}}{v_{2}}=frac{1+e}{1-e} ) B. ( frac{v_{1}}{v_{2}}=frac{1-e}{1+e} ) c. ( frac{v_{1}}{v_{2}}=frac{1+e}{2} ) D. ( frac{v_{1}}{v_{2}}=frac{1-e}{2} ) | 11 |

123 | A particle of mass M is moving in a horizontal circle of radius R with uniform speed ( V ). when it moves from one point to a diametrically opposite point, its A. kinetic energy changes by ( M V^{2} / 4 ) B. momentum does not change c. momentum changes by 2 MV D. kinetic energy changes by ( M V^{2} ) | 11 |

124 | Energy possessed by a body due to its motion is: A. kinetic energy B. nuclear energy c. potential energy D. thermal energy | 11 |

125 | A bullet of mass 2.5 g moving with a velocity of ( 500 m s^{-1}, ) enters a wooden block and comes out of it with a velocity of ( 100 m s^{-1} . ) Find the work done by the bullet while passing through the wooden block. A. 100 J B. 300 J c. ( 500 mathrm{J} ) D. 800 J | 11 |

126 | A system absorbs ( 600 mathrm{J} ) of energy and does work equivalent to ( 400 mathrm{J} ) of energy. The internal energy change is A . 1000 B. 200 J c. ( 600 mathrm{J} ) D. 300 J | 11 |

127 | Shape of graph between speed and kinetic energy of the body is: A. Hyperbola B. Straight line c. Parabola D. circle | 11 |

128 | A particle of mass ( m_{1} ) is projected to the right with a speed ( v_{1} ) onto a smooth wedge of mass ( m_{2} ) which is simultaneously projected due to the left with a speed ( v_{2} ). Highest point on the wedge attained by the particle is ( frac{boldsymbol{m}_{2}left(boldsymbol{v}_{1}+boldsymbol{v}_{2}right)^{2}}{boldsymbol{x} boldsymbol{g}left(boldsymbol{m}_{1}+boldsymbol{m}_{2}right)} cdot ) Find ( boldsymbol{x} ) | 11 |

129 | The mass of the moon is ( 1 % ) of mass of the earth.The ratio of gravitational pull of earth on moon to that of moon on earth will be: A . 1: B. 1: 10 c. 1: 100 D. 2:1 | 11 |

130 | A smooth body is released from rest at a point ( A ) at the top of a smooth curved track of vertical height ( 40 mathrm{cm} . ) What is the speed of the body at the bottom of the curved track? How far along the adjoining smooth inclined plane will the body go? | 11 |

131 | toppr Q Type your question graph correctly shows the momentum of the blue object in each case. The red graphs are all different. Which graph best represents the possible momentum of the red object before, during, and after the collision? ( A ) ( B ) ( c ) ( D ) E | 11 |

132 | Mark correct answer | 11 |

133 | A body of mass ( 20 mathrm{kg} ) is at rest. A force of ( 5 mathrm{N} ) applied on it. Calculate the work done in the first second | 11 |

134 | Find the component of ( vec{r} ) in the direction of ( vec{a}: ) A ( cdot frac{(vec{r} cdot vec{a}) vec{a}}{a^{2}} ) B. ( frac{(vec{r} cdot vec{a}) vec{a}}{a} ) c. ( frac{(vec{r} times vec{a}) vec{a}}{a^{2}} ) D. None of above | 11 |

135 | 1. Referring the graphs, which of the following is/are correct? 1 1 2 3 U Fig. 8.273 a. The particle has stable equilibrium at points 3 and b. b. The particle is in neutral equilibrium at points b and c. No power is delivered by the force on the particle at points 1, 3, and b. d. The particle has least kinetic energy at position 1. | 11 |

136 | wul walking upoll a staircase. 20. A man of mass m is standing on a stationary flat car or mas M. The car can move without friction along horizontal rails. The man starts walking with velocity v relative to the car. Work done by him a. is greater than-mv2 if he walks along rails. b. is less than-mv2 if he walks along rails. c. is equal to mv2 if he walks normal to rails. d. can never be less than | 11 |

137 | Assertion The kinetic energy, with any reference, must be positive. Reason In the expression for kinetic energy, the velocity appears with power 2 A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

138 | A particle of mass ( m ) is in UCM of radius ( r ) and has momentum equal to ( P . ) Its ( mathrm{KE} ) is equal to: ( ^{mathrm{A}} cdot frac{P^{2}}{2 m} ) в. ( frac{P^{2}}{m} ) c. ( frac{P}{2 m} ) D. ( frac{P}{m} ) | 11 |

139 | ( m_{2}=2 k g ) are connected by an ideal spring, rest on a rough horizontal surface. The spring is unstressed. The spring constant of spring is ( boldsymbol{K}=mathbf{2} boldsymbol{N} / boldsymbol{m} . ) The coefficient of friction between blocks and horizontal surface is ( mu=frac{1}{2} . ) Now the left block is imparted a velocity ( u ) towards right as shown. The largest value of ( u(text { in } m / s) ) such that the block of mass ( m_{2} ) never moves is (Take ( g= ) ( left.10 m / s^{2}right) ) A . 10 B. 20 ( c .5 ) D. | 11 |

140 | If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{i}-4 hat{j}+alpha hat{k}, ) then value of ( boldsymbol{alpha} ) is: A . -1 в. ( frac{1}{2} ) ( c cdot-frac{1}{2} ) D. 1 | 11 |

141 | The angle between the vectors ( (hat{i}+hat{j}+ ) ( hat{boldsymbol{k}}) ) and ( (hat{boldsymbol{i}}-hat{boldsymbol{j}}-hat{boldsymbol{k}}) ) is: A ( cdot sin ^{-1} frac{sqrt{8}}{3} ) в. ( sin ^{-1} frac{1}{3} ) c. ( cos ^{-1} frac{sqrt{8}}{3} ) D. ( cos ^{-1} sqrt{frac{8}{3}} ) | 11 |

142 | Rahul is standing on the street and wants to throw an ( 8 k g ) book up to his friend who is leaning out of a window ( 5 m ) above street level. With what velocity Rahul must throw the book so that it reaches his friend in the window? A. ( 5 m / s ) в. ( 8 m / s ) c. ( 10 m / s ) D. ( 40 mathrm{m} / mathrm{s} ) E ( .50 mathrm{m} / mathrm{s} ) | 11 |

143 | A particle is moving in a potential region given by ( U=Kleft(x^{2}+y^{2}+z^{2}right) ) The force acting on the particle is given by: A . ( -2 K(x hat{i}+y hat{j}+z hat{k}) ) B . ( K(x hat{i}+y hat{j}+z hat{k}) ) c. ( frac{K}{2}(x hat{i}+y hat{j}+z hat{k}) ) D. ( Kleft(x^{2} hat{imath}+y^{2} hat{jmath}+z^{2} hat{k}right) ) | 11 |

144 | A torch converts energy to energy. A. chemical, heat B. electrical, chemical c. chemical, light D. light, electrical | 11 |

145 | A cyclist wants to loop the loop inside the death globe of diameter 5 m. Find the minimum velocity, that he should have at the lowest point and calculate the height from which he should start it. ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) | 11 |

146 | 9. The potential energy of the man a. Increases by mg(i-h) b. Increases by mg! c. Increases by mgh d. Increases by mg (21 – h) | 11 |

147 | 4 A ball of mass m moving with a velocity u rebounds from a wall. The collision is assumed to be elastic and the force of interaction between the ball and wall varies as shown in Fig. 6.296. Then the value of F, is AF G – 0.5 T T Fig. 6.296 b. 2 mu/T c. 4 mu/T d. mu/2 T a. mu/T | 11 |

148 | A ball with momentum ( 0.5 k g m s^{-1} ) coming towards a batsman is hit by him such that it goes on the same path in opposite direction with momentum ( 0.3 k g m s^{-1} . ) If the time of contact of the ball with the bat is ( 0.02 s ), find the force on the ball by the bat. A . ( 10 N ) в. ( 40 N ) ( c .75 N ) D. 30 N | 11 |

149 | Which of the following does not possess the ability to do work not because of motion? A. A sparrow flying in the sky. B. A sparrow moving slowly on the ground. c. A sparrow in the nest on a tree D. A squirrel going up a tree | 11 |

150 | A spring ( left(k=100 N m^{-1}right) ) is suspended in vertical position having one end fixed at top ( & ) other end joined with a ( 2 mathrm{kg} ) block. When the spring is in non deformed shape, the block is given initial velocity ( 2 mathrm{m} / mathrm{s} ) in downward direction. The maximum elongation of the spring is ( left(frac{sqrt{3}+1}{n}right) ) meter. Find ( n ) | 11 |

151 | When a stone is thrown upwards: A. Kinetic energy increases and Potential energy decreases B. both Kinetic energy and Potential energy increase C. Kinetic energy decreases and Potential energy increases D. both remain constant | 11 |

152 | What are the limitations of the energy obtained from oceans(any two)? | 11 |

153 | A ( 90 mathrm{gm} ) ball moving at ( 100 mathrm{cm} / mathrm{s} ) collide head on with a stationary 10 gm ball. The coefficient of restitution is ( 0.5 . ) Their respective velocities after collision are A ( cdot 135 mathrm{cm} / mathrm{s}, 85 mathrm{cm} / mathrm{s} ) B. ( 85 mathrm{cm} / mathrm{s}, 135 mathrm{cm} / mathrm{s} ) ( c .-85 mathrm{cm} / mathrm{s}, 135 mathrm{cm} / mathrm{s} ) D. ( 85 mathrm{cm} / mathrm{s},-135 mathrm{cm} / mathrm{s} ) | 11 |

154 | Given figure shows the vertical section of a frictionless surface. A block of mass ( 2 mathrm{kg} ) is released from the position A, its kinetic energy as it reaches the position C is A ( .180 mathrm{J} ) В. 140 c. ( 40 mathrm{J} ) D. 280 | 11 |

155 | For a particle projected in a transverse direction from a height h above earth’s surface, find the minimum initia velocity so that it just grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth’s surface as perigee. | 11 |

156 | The muscular energy required by our body is given to us by: A. Air B. water c. oxygen D. Food | 11 |

157 | A body is acted upon by a force which is proportional to the distance covered. If distance covered is represented by ( s ) then work done by the force will be proportional to. ( A ) B ( cdot s^{2} ) c. ( sqrt{s} ) D. None of the above | 11 |

158 | A body is moving with a velocity 1 ms ( ^{-1} ) a force ( F ) is needed to stop it within a distance ( x ). If the speed of the body is ( 3 m s^{-1}, ) the force needed to stop it with in the same distance ( (x) ) will be: A ( .9 F ) в. ( 6 F ) ( c .3 F ) D. ( 1.5 F ) | 11 |

159 | The distance of the centre of mass of the system from the centre of bigger sphere at the moment of collision is 4 3.27 ( c cdot 3 r ) D. 47 | 11 |

160 | K. ( boldsymbol{E} ) of a body can be calculated by the amount of work done in stopping the moving body or by the amount of the work done in imparting the present velocity to the body from the state of rest | 11 |

161 | ( ln C H_{4} ) molecule, there are four ( C-H ) bonds. If two adjacent bonds are in ( hat{mathbf{i}}+ ) ( hat{boldsymbol{j}}+hat{boldsymbol{k}} ) and ( hat{boldsymbol{i}}-hat{boldsymbol{j}}-hat{boldsymbol{k}} ) direction, then find the angle between these bonds. A ( cdot sin ^{-1}left(frac{-1}{3}right) ) B. ( cos ^{-1}left(frac{1}{3}right) ) ( ^{c} cdot sin ^{-1}left(frac{1}{3}right) ) D. ( cos ^{-1}left(frac{-1}{3}right) ) | 11 |

162 | What is the angle between ( (hat{mathbf{i}}+hat{boldsymbol{j}}+hat{boldsymbol{k}}) ) and ( hat{i} ? ) A ( cdot frac{pi}{6} ) в. ( frac{pi}{4} ) ( c cdot frac{pi}{3} ) D. ( cos ^{-1}left(frac{1}{sqrt{3}}right) ) | 11 |

163 | A marble starts falling from rest on a smooth inclined plane of inclination ( alpha ) After covering distance ( h ) the ball rebounds off the plane. The distance from the impact point where the ball rebounds for the second time is : ( A cdot 8 h cos alpha ) B. ( 8 h sin alpha ) ( c cdot 2 h tan alpha ) D. ( 4 h sin alpha ) | 11 |

164 | In Fig. 8.246, the variation of potential energy of a particle of mass m= 2 kg is represented w.r.t its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. Which of the following statements is incorrect about the particle? 1 UG) 20 —- 15 x(m) ca -15 Fig. 8.246 a. If it is released at the origin, it will move in negative x-axis. b. If it is released at x = 2 + A, where A → 0, then its maximum speed will be 5 ms’ and it will perform oscillatory motion. c. If initially x = -10 and ū= v6i, then it will cross x = 10. d. x=-5 and x = +5 are unstable equilibrium positions of the particle. | 11 |

165 | A ( 10-k g ) block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius ( 10 mathrm{m} ) The applied force is ( 200 N ) as shown in the figure.If the block started from rest at ( A, ) the velocity at ( B ) would be A . ( 1.732 mathrm{m} / mathrm{s} ) B. ( 17.32 mathrm{m} / mathrm{s} ) c. ( 173.2 mathrm{m} / mathrm{s} ) D. none of these | 11 |

166 | A ball of mass ( m ) moving with velocity ( v ) collides elastically with another ball of identical mass coming from opposite direction with velocity ( 2 v ). Their velocities after collision will be : A. ( -v, 2 v ) В. ( -2 v, v ) c. ( v,-2 v ) D. ( 2 v,-v ) | 11 |

167 | A plane surface is inclined at an angle of ( 60^{0} ) with the horizontal. A body of mass ( 10 mathrm{kg} ) is uniformly accelerating, along the inclined plane surface. The value of coefficient of friction ( mu_{k} ) between the body and the inclined surface is ( 0.2, ) if the length of the inclined plane is ( 10 mathrm{m} ), then the work done to pull it to the top is ( Take ( boldsymbol{g}= ) ( 10 m / s^{2} ) A . 666 J B. 766 J c. 866 J D. 966 J | 11 |

168 | A body of mass ( 1 k g ) is thrown upwards with a velocity ( 20 m / s . ) It momentarily comes to rest after attending a height of ( 18 m . ) How much energy is lot due to air friction (in J) A . 10 B. 20 ( c .30 ) D. 40 | 11 |

169 | A ball P moving with a speed of ( boldsymbol{v} boldsymbol{m} boldsymbol{s}^{-1} ) collides directly with another identical ball Q moving with a speed ( 10 mathrm{ms}^{-1} ) in the opposite direction. P comes to rest after the collision. If the coefficient of restitution is ( 0.6, ) the value of ( v ) is: A ( cdot 30 m s^{-1} ) B. ( 40 mathrm{ms}^{-1} ) c. ( 50 m s^{-1} ) D. ( 60 m s^{-1} ) | 11 |

170 | Which of the following are correct? This question has multiple correct options ( mathbf{A} cdot ) If ( R ) is the radius of a planet, ( g ) is the acceleration due to gravity, the mean density of the planet is ( 3 g / 4 pi G R ) B. Acceleration due to gravity is a universal constant. C. The escape velocity of a body from earth is ( 11.2 mathrm{km} mathrm{s}^{-1} ) The escape velocity from a planet which has double the mass of earth and half its radius is ( 22.4 mathrm{km} mathrm{s}^{-1} ) D. The ratio of gravitational mass and inertial mass of a body at the surface of earth is 1 | 11 |

171 | The work done to pull them (the molecules apart if they are at ( R_{0}, ) is: A. ( U_{0} ) в. ( 2 U_{0} ) c. ( -2 U_{0} ) D. none | 11 |

172 | If the vectors ( vec{A}=a hat{i}+hat{j}-2 hat{k} ) and ( hat{B}= ) ( boldsymbol{a} hat{boldsymbol{i}}-boldsymbol{a} hat{boldsymbol{j}}+hat{boldsymbol{k}} ) are perpendicular to each other then the positive value then the positive value of ‘a’ is A. zero в. ( c cdot-1 ) D. 3 | 11 |

173 | A retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance travelled when same retarding force is applied is A. The same B. Doubled c. Halved D. Four times | 11 |

174 | If ( a, b ) and ( c ) are three non-zero vectors such that ( a cdot|b times c|=0 ) and ( b ) and ( c ) are not parallel then ( a, b ) and ( c ) are A. Collinear B. Coplanar c. May be both D. None | 11 |

175 | The relationship between force and position is shown in the figure (in one dimensional case). Work done by the force in displacing a body from ( x=1 mathrm{cm} ) to ( x=5 c m ) is : A. 700 erg B. 70 erg c. 60 erg D. 20 erg | 11 |

176 | Complete the following statement. The work done on a system: A. always changes the potential energy of the system B. always changes the kinetic energy of the system C. always changes the momentum of a system D. can change either the potential energy or kinetic energy of the system E. is not related to the energy of the system. | 11 |

177 | If two balls each of mass ( 0.06 mathrm{kg} ) moving in opposite directions with speed of ( 4 m s^{-4} ) collide and rebound with same speed, then the impulse imparted to each ball due to other is: A ( .0 .48 mathrm{kg} mathrm{m} mathrm{s}^{-1} ) в. 0.53 kg ( m s^{-1} ) c. ( 0.8 mathrm{kg} mathrm{m} mathrm{s}^{-1} ) D. ( 0.92 mathrm{kg} mathrm{m} mathrm{s}^{-1} ) | 11 |

178 | A body of mass ( 2 k g ) is projected vertically upwards with speed of ( 3 m / s ) The maximum gravitational potential energy of the body is (in J) A . 18 в. 4.5 c. 9 D. 2.5 | 11 |

179 | From one corner A of a rectangular billiard table ABCD placed on a horizontal surface, a ball of mass and negligible dimension is projected in the direction making ( theta ) with side ( A B ) it strikes in other sides ( mathrm{BC}, mathrm{AD}, mathrm{DC} ) and ( mathrm{BC} ) and then return to same point A. Then the value of coefficient of restitution is: ( A ) в. ( sqrt{frac{a sin theta}{b cos theta+a sin theta}} ) c. ( sqrt{frac{a sin theta}{b sin theta-a cos theta}} ) D. ( sqrt{frac{a sin theta}{b sin theta+a cos theta}} ) | 11 |

180 | 33. The ratio of the energy consumed by the camel during uniform motion for the two cases when it moves with speed 5 ms to the case when it moves with 10 ms b. 19 a 10 a 20 a. 19 19 . c. 10 10 | 11 |

181 | Due to a force of ( (6 hat{i}+2 hat{j}) mathrm{N} ) the displacement of a body is ( (3 hat{i}-hat{j}) m ) then the work done is? A . 16 в. 12 ( c .8 ) D. zero | 11 |

182 | A ball tied at the end of a string and swinging back and forth, at what point in the swing would the ball have the highest potential energy? A. At the bottom of the swing B. Mid way between the bottom and the top of the swing c. At the top of the swing D. just past the bottom of the swing on the way up E. Just past the top of the swing on the way back down | 11 |

183 | * ULUULUULUU 13. A ring of mass m= 1 kg can slide over a smooth vertical rod. A light string attached to the ring passing over a smooth fixed pulley at a distance of L = 0.7 m from the rod as shown in Fig. 8.217. 2 370 Fig. 8.217 At the other end of the string mass M= 5 kg is attached, lying over a smooth fixed inclined plane of inclination angle 37º. The ring is held in level with the pulley and released. Determine the velocity of ring when the string makes an angle (a=37°) with the horizontal. [sin 37° = 0.6] | 11 |

184 | Which of the following is not an example of perfectly inelastic collision? A. A bullet fired into a block, if bullet gets embedded into block B. Capture of an electron by an atom c. A man jumping onto a moving boat D. A ball bearing striking another ball bearing | 11 |

185 | The example given in the problem represents collision. A. elastic B. partially inelastic c. perfectly inelastic D. none | 11 |

186 | ( N ) similar slabs of cubical shape of edge ( b ) are lying on ground. Density of material of slab is ( rho . ) Work done to arrange them one over the other is A ( cdotleft(N^{2}-1right) b^{3} rho g ) B. ( (N-1) b^{4} rho g ) c. ( frac{1}{2}left(N^{2}-Nright) b^{4} rho g ) D. ( left(N^{2}-Nright) b^{4} rho g ) | 11 |

187 | A body of mass ( 3 mathrm{kg} ) is under a constant force which causes a displacement s in metres in it,given by the relation ( s= ) ( frac{1}{2} t^{2}, ) where ( t ) is in seconds. Work done by the force in 2 seconds is:- A ( cdot frac{5}{19} ) в. ( frac{3}{8} ) 」 ( c cdot frac{8}{3} ) D. ( frac{19}{5} ) | 11 |

188 | Once a choice made regarding zero potential energy reference state, the change in potential energy is : A . same B. different c. depend strictly on the choice of zero potential D. become indetermine | 11 |

189 | 3. A bead is free to slide down on a smooth wire rightly stretched between points A and B on a vertical circle of radius 10 m. Find the time taken by the bead to reach point B, if the bead slides from rest from the highest point A on the circle. Fig. 5.209 | 11 |

190 | An object of mass ( m ) slides down a hil of height ( h ) and of arbitrary shape and stop at the bottom because of friction. The coefficient of friction may be different for different segments of the path. Find the work required to return the object to its initial position along the same path by by a tangential force A ( . m g h ) в. 2 тун c. ( -m g h ) D. It cant be calculated | 11 |

191 | 3. One of the forces acting on a particle is conservative, then a. Its work is zero when the particle moves exactly once around any closed path. b. Its work equals the change in the kinetic energy of the particle. c. It does not obey Newton’s second law. d. Its work depends on the end points of the motion, not on the path in between. | 11 |

192 | When the displacement of a particle executing SHM is one – fourth of its amplitude, what fraction of the total energy is the kinetic energy? A ( cdot frac{16}{15} ) в. ( frac{15}{16} ) ( c cdot frac{3}{4} ) D. ( frac{4}{3} ) | 11 |

193 | Choose the correct statement from the following: This question has multiple correct options A. Kinetic energy of a body is quadrupled, when its velocity is doubled. B. Kinetic energy is proportional to square of velocity. C. Kinetic energy does not depend on mass of the body. D. The change in kinetic energy of a particle is equal to the work done on it by the net force. | 11 |

194 | Two identical 5 kg blocks are moving with same speed of ( 2 m / s ) towards each other along a friction-less horizontal surface. The two blocks collide, stick together and come to rest. Consider two blocks as a system, the work done on the system by the external forces will be: A . 20 Joule B . -20 Joule c. 0 Joule D. None of these | 11 |

195 | A particle of mass ( 0.1 mathrm{kg} ) moving with an initial speed v collides with another particle of same mass kept at rest. If after collision the total energy becomes ( 0.2 mathrm{J}, ) then: A. minimum value of v is ( 2 mathrm{m} / mathrm{s} ) B. maximum value v is 4 ( mathrm{m} / mathrm{s} ) c. minimum value v is 3 ( mathrm{m} / mathrm{s} ) D. maximum value of v is ( 6 mathrm{m} / mathrm{s} ) | 11 |

196 | A plastic ball is dropped from a height of ( 1 m ) and rebounds several times from the floor. If 0.13 sec elapse from the moment it is dropped to the second impact with the floor, what is the coefficient of restitution? A . 0.85 B. 0.25 c. 0.39 D. 0.65 | 11 |

197 | A car of mass ( 1200 mathrm{kg} ) is moving with a speed of ( 81 mathrm{km} / mathrm{hr} ). Calculate its kinetic energy. | 11 |

198 | A body of mass ( m_{1} ) moving with an unknown velocity of ( v_{1} hat{i}, ) undergoes a collinear collision with a body of mass ( m_{2} ) moving with a velocity ( v_{2} hat{i} ). After collision, ( m_{1} ) and ( m_{2} ) move with velocities of ( v_{3} hat{i} ) and ( v_{4} hat{i}, ) respectively. If ( m_{2}=0.5 m_{1} ) and ( v_{3}=0.5 v_{1}, ) then ( v_{1} ) is : A ( cdot v_{4}-frac{v_{2}}{4} ) B. ( v_{4}-frac{v_{2}}{2} ) ( mathbf{c} cdot v_{4}-v_{2} ) ( mathbf{D} cdot v_{4}+v_{2} ) | 11 |

199 | A shown in figure there is a spring block system. Block of mass ( 500 mathrm{g} ) is pressed against a horizontal spring fixed at one end to compress the spring through 5.0 cm. The spring constant is ( 500 mathrm{N} / mathrm{m} ) When released, the block moves horizontally till it leaves the spring Calculate the distance where it will hit the ground 4 m below the spring? ( A cdot 6 m ) в. ( 4 m ) ( c .8 m ) ( D cdot sqrt{2} m ) | 11 |

200 | A Nall Ul mass U.c ng resus un diverica post of height ( 5 mathrm{m} ). A bullet of mass 0.01 kg, traveling with a velocity ( V m / s ) in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of ( 20 m ) and the bullet at a distance of ( 100 mathrm{m} ) from the foot of the post. The initial velocity ( V ) of the bullet is ( A cdot 250 m / s ) B . ( 250 sqrt{2} mathrm{m} / mathrm{s} ) c. ( 400 mathrm{m} / mathrm{s} ) D. ( 500 mathrm{m} / mathrm{s} ) | 11 |

201 | If ( mathbf{W}_{1}, mathbf{W}_{2} ) and ( mathbf{W}_{3} ) represent the work done in moving a particle from ( A ) to ( B ) along three different paths 1,2 and 3 respectively (as shown) in the gravitational field of a point mass ( mathbf{m} ) find the correct relation between ( mathbf{W}_{1}, mathbf{W}_{2} ) and ( mathbf{W}_{3} ) A. ( mathrm{W}_{1}>mathrm{W}_{2}>mathrm{W}_{3} ) B. ( mathrm{W}_{1}=mathrm{W}_{2}=mathrm{W}_{3} ) c. ( mathrm{w}_{1}<mathrm{W}_{2}mathrm{W}_{1}>mathrm{W}_{3} ) | 11 |

202 | Two identical balls each of mass in are moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is : A. 0 в. ( frac{1}{2} m v^{2} ) ( mathrm{c} cdot m v^{2} ) ( mathbf{D} cdot 2 m v^{2} ) | 11 |

203 | 14. The maximum kinetic energy of the particle and the value of x at which maximum kinetic energy occurs are a. 29 J,0 m b. 49 J, 0 m c. 49 J, 2 m d. 29 J, 2 m | 11 |

204 | 24. Which of the following statements is/are correcta work? a. In a certain reference frame, W pseudo force + W conservative force + W non-conservative force + Wother forces = AK b. Work done by friction is always negative. c. Work done by a force is defined as the dot product of the force and the displacement of the point of application of force. d. Work done by conservative force in moving a body from A to B = potential energy of the body at A – potential energy of the body at B. . . cita nainen | 11 |

205 | A uniform rod ( A B ) which is free to swing in the vertical plane about a horizontal axis through ( A, ) is hanging freely. ( A ) particle of equal mass strikes the rod with a velocity ( V_{0} ) and gets stuck to it.Find the angular velocity of the combination immediately after the collision. | 11 |

206 | Which of the following will lead to a change in kinetic energy of a body? A. change in its mass c. change in its velocity D. all of the above | 11 |

207 | A particle of mass ‘ ( m^{prime} ) and charge ( ^{prime} q^{prime} ) is accelerated through a potential difference of ( ^{prime} V^{prime} ) volt. Its energy is… A ( . q V ) в. ( m q V ) c. ( left(frac{q}{m}right) v ) D. ( frac{q}{m V} ) | 11 |

208 | Calculate the work done when a 2N force moves a body through a distance of ( 10 mathrm{m} ) A . 10 B. 2 J c. 5 J D. 20 | 11 |

209 | The value of ratio ( M / m ) is 4. 2: 3 B . 3: 2 ( c cdot 4: 3 ) D. 3: 4 | 11 |

210 | Which of the following does not have potential energy? A. An inflated balloon B. Water in a flowing river c. A fruit on the tree D. A spinning top | 11 |

211 | The work done by all the forces on a system equals the change in A. total energy. B. kinetic energy. c. potential energy. D. none of these | 11 |

212 | A body is dropped from a certain height from the ground. When it is halfway down, it possess, A. Only K.E. B. Both K.E. and P.E. c. only P.E. D. zero energy | 11 |

213 | Assertion (A): When a ball hits a floor obliquely and gets reflected after inelastic collision, only the vertical component of its velocity gets changed. Reason (R): During collision the floor exerts a force on the ball only along the normal but not parallel to the surface A. Both Assertion (A) and Reason (R) are correct and R is the correct explanation B. Both Assertion (A) and Reason (R) are correct but the reason does not give the correct explanation c. A is true but R is false D. A is false but R is true | 11 |

214 | Quantities remaining constant in a collision are A. Momentum, kinetic energy and temperature B. Momentum but not kinetic energy and temperature C. Kinetic energy and temperature but not momentum D. None | 11 |

215 | What is potential energy? A. Energy of an abject due to its position or arrangement in a system B. Energy of an abject due to its nature or arrangement in a system C. Energy of an abject due to its shape or arrangement in a system D. None | 11 |

216 | If the initial speed of the cars is ( x mathrm{m} / mathrm{s} ) find ( 2 x ) | 11 |

217 | A boy a wagon along a horizontal surface for a distance of 10.0 meters. The boy applies a force of 15 N straight along the handle while the wagon moves, and the handle makes an angle of 35 degrees with the horizontal. How much work does the boy do on the wagon? | 11 |

218 | The potential energy of a particle of mass ( 5 mathrm{kg} ) moving in the ( mathrm{x} ) -y plane is given by the equation, ( U=-7 x+24 y ) Joule. Here ( x ) and ( y ) are in the meter at ( t=0, ) the particle is at the origin and moving with velocity ( (2 hat{i}+3 hat{j}) m / s . ) The magnitude of acceleration of particle is ( mathbf{A} cdot 3 m / s^{2} ) B . ( 5 mathrm{m} / mathrm{s}^{2} ) D. ( 15 mathrm{m} / mathrm{s}^{2} ) | 11 |

219 | A particle is moving in a circular path of radius a under the action of an attractive potential ( U=-frac{K}{2 r^{2}} . ) Its total energy is | 11 |

220 | A force acts on a body and displaces it in it’s direction. The graph shows the relation between the force and displacement. The work done by the force is: ( mathbf{A} cdot 420 J ) B. ( 360 J ) c. ( 840 J ) D. ( 720 J ) | 11 |

221 | Two bodies of equal weight are kept at heights of h and 1.5 h respectively. The ratio of their P.E. will be: A . 3: 2 B. 2: 3 c. 1: D. none of these | 11 |

222 | The resultant of ( vec{A} ) and ( vec{B} ) makes an angle ( alpha ) with ( vec{A} ) and an angle ( beta ) with ( vec{B} ) then :- ( mathbf{A} cdot alpha<beta ) B. ( alpha<beta ) if ( A<B ) c. ( alphaB ) D. ( alpha<beta ) if ( A=B ) | 11 |

223 | Sphere (1) moving with velocity ( 4 mathrm{m} / mathrm{s} ) collides another sphere (2) at rest. Find final velocity of sphere (1) after collision collision perfectly elastic ( A cdot 2 hat{imath}+sqrt{3} hat{jmath} ) B . ( 2 hat{i}-sqrt{3} hat{j} ) ( c cdot hat{i}+sqrt{3} hat{j} ) D. ( hat{i}-sqrt{3} hat{j} ) | 11 |

224 | A ball of mass ( 200 g ) falls from a height of ( 5 m . ) What is its K.E. when it just reaches the ground? A . ( 9.8 J ) в. ( 98 J ) ( mathrm{c} .980 mathrm{J} ) D. None of these | 11 |

225 | A cannon of mass ( 10 times 10^{3} k g ) is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a ( 2.1 times 10^{3} k g ) shell horizontally with an initial velocity of ( 550 m / s . ) Suppose the cannon is then unbolted from the earth and no external force hinder its recoil. What would be the velocity (in ( boldsymbol{m} / boldsymbol{s} ) ) of a shell fired horizontally by the loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.) | 11 |

226 | A mass is at the center of a square, with four masses at the corners as shown. Rank the choices according to the magnitude of the gravitational force on the center mass. ( mathbf{A} cdot F_{A}=F_{B}F_{B}<F_{D}F_{C}=F_{D} ) D. None | 11 |

227 | The potential energy of 1 kg particle free to move along the X-axis is given by ( boldsymbol{U}=left(frac{boldsymbol{x}^{4}}{boldsymbol{4}}-frac{boldsymbol{x}^{2}}{mathbf{2}}right) boldsymbol{J} ) The total mechanical energy of the particle is 2 J. Then Maximum speed of the particle is : A ( cdot frac{3}{sqrt{2}} ) B. ( frac{1}{sqrt{2}} ) ( c cdot sqrt{2} ) D. 2 | 11 |

228 | A car of mass ( m ) starts moving so that its velocity varies according to the law ( boldsymbol{v}=boldsymbol{beta} sqrt{boldsymbol{s}}, ) where ( boldsymbol{beta} ) is a constant, and ( boldsymbol{s} ) is the distance covered. The total work performed by all the forces which are acting on the car during the first ( t ) seconds after the beginning of motion is: ( mathbf{A} cdot m beta^{4} t^{2} / 8 ) B ( cdot m beta^{2} t^{4} / 8 ) ( mathbf{c} cdot m beta^{4} t^{2} / 4 ) ( mathbf{D} cdot m beta^{2} t^{4} / 4 ) | 11 |

229 | A person holds a bucket of weight ( 60 N ) He walks ( 7 m ) along the horizontal path and then climbs up a vertical distance of 5 m. The work done by the man is: A . ( 300 J ) в. ( 420 J ) c. ( 720 J ) D. none of these | 11 |

230 | When two bodies collide elastically then the quantity conserved is: A. kinetic energy B. mometum c. both D. none | 11 |

231 | If two vectors ( 2 hat{i}+3 hat{j}+3 hat{k} ) and ( -4 hat{i}- ) ( 6 hat{j}+lambda hat{k} ) are parallel to each other then value of ( lambda ) is A . -6 B. – ( c .-3 ) D. -4 | 11 |

232 | Law of conservation of energy states that : A. energy cannot be destroyed but can be created and transformed from one form to another B. enerry exists in only one form C. energy exists in many forms but it cannot be transformed D. energy can neither be created nor be destroyed but can be transformed from one form to another | 11 |

233 | * *.162507,power transmite sebe sampel to load is 32. Maximum power transmitted by the camel to load is a. 6250 Js- b. 5000 JS- c. 10 Js-1 d. 1250 JS- | 11 |

234 | A block of mass ( m ) is pulled slowly by a minimum constant force ( (boldsymbol{F}) ) on a horizontal surface through a distance ( x ) The coefficient of kinetic friction is ( mu ) Find the work done by the force ( (boldsymbol{F}) ) | 11 |

235 | An ( 8 k g ) cat is dragged along a hardwood floor such that her final velocity is ( 80 mathrm{cm} / mathrm{s} ) after being dragged through ( 2 m ) She is initially at rest. In this time interval, the work done on the cat by the normal force exerted by the floor is closest to: A. zero в. ( 1.88 J ) c. ( 2.56 J ) D . 78.48J E . 156.965 | 11 |

236 | Data force ( , f=2 hat{i}+3 hat{j}-4 hat{k} ) displacement ( s=2 hat{i}+3 hat{j}-4 hat{k} ) find work? | 11 |

237 | A particle of mass ( m ) initially moving with speed ( v . A ) force acts on the particle ( boldsymbol{f}=boldsymbol{k} boldsymbol{x} ) where ( boldsymbol{x} ) is the distance travelled by the particle and ( k ) is constant. Find the speed of the particle when the work done by the force equals ( W ) A ( cdot sqrt{frac{k}{m}+v^{2}} ) B. ( sqrt{frac{2 W}{m}+v^{2}} ) c. ( sqrt{frac{2 W}{k}+v^{2}} ) D. ( sqrt{frac{W}{2 m}+v^{2}} ) | 11 |

238 | The particle executing simple harmonic motion has a kinetic energy ( K_{0} cos ^{2} omega t ) The maximum values of the potential energy and the total energy are respectively A. ( K_{0} ) and ( K_{0} ) B. 0 and ( 2 K_{0} ) c. ( frac{K_{0}}{2} ) and ( K_{0} ) D. ( K_{0} ) and ( 2 K_{0} ) | 11 |

239 | In stretching a spring by ( 2 mathrm{cm} ) energy stored is given by ( U, ) then stretching by ( 10 mathrm{cm} ) energy stored will be : A. ( U ) B. ( 5 U ) c. ( frac{U}{25} ) D. 25U | 11 |

240 | Two balls of mass ( m_{1} ) and ( m_{2} ) where ( m_{2}=0.5 m_{1}, ) undergo head on collision as shown in figure. If ( boldsymbol{v}_{3}=mathbf{0 . 5} boldsymbol{v}_{1} ) value of ( boldsymbol{v}_{4} ) is fter collision A ( cdot v_{4}=v_{1}+v_{2} ) B ( cdot v_{4}=v_{1}+2 v_{2} ) ( mathbf{c} cdot v_{4}=2 v_{1}+v_{2} ) ( mathbf{D} cdot v_{4}=2 v_{1}+3 v_{2} ) | 11 |

241 | The energy directly related to the speed of a moving body and its mass is: A. Kinetic B. Potential c. solar D. Electric | 11 |

242 | Initially spring is relaxed. A person starts pulling the spring by applying a variable force ( F ). Where has the work gone? A. It is stored in the form of thermal energy in spring B. It is stored in the form of potential energy in spring C. It is stored in the form of kinetic energy in spring D. Cannot be determined | 11 |

243 | A frame of mass ( 200 g ) when suspended from a massless spring extends it by 10 ( c m . ) A lump of clay of mass ( 200 g ) is dropped from rest on to the frame from a height of ( 30 mathrm{cm} ) as shown in figure. What is the maximum distance through which pan moves downwards? | 11 |

244 | A machine, which is 75 percent efficient uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to fall through that distance. What will its velocity be at the end of its fall? A ( cdot sqrt{32} mathrm{m} / mathrm{s} ) B. ( sqrt{24} m / s ) c. ( sqrt{18} mathrm{m} / mathrm{s} ) D. ( sqrt{9} m / s ) | 11 |

245 | Define kinetic energy. | 11 |

246 | A ball of mass ( M ) falls from a height ( h ) on a floor which the coefficient of restitution is ( e . ) The height attained by the ball after two rebounds is: ( mathbf{A} cdot e^{2} h ) B ( cdot e h^{2} ) ( mathbf{c} cdot e^{4} h ) D. ( frac{h}{e^{4}} ) | 11 |

247 | The slope of Kinetic Energy displacement curve of a particle in motion is: A. equal to the acceleration of the particle B. inversely proportional to the acceleration c. directly proportional to the acceleration D. none of these | 11 |

248 | A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then? A. Lorry will come to rest in a shorter distance B. Car will come to rest in a shorter distance c. Both come to restin a same distance D. None of the above | 11 |

249 | A ( 250 g ) block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of ( 40 mathrm{cm} / mathrm{s} ). If the friction coefficient between the table and the block is 0.1 how far does the block move before coming to rest? | 11 |

250 | A ball is dropped from a height ( 100 m ) on the ground. If the coefficient of restitution is ( 0.2, ) the height to which the ball will go up after it rebounds for the IInd time A . ( 15 m ) B. ( 1.6 mathrm{cm} ) ( c .1 .6 m ) D. ( 40 mathrm{cm} ) | 11 |

251 | If the maximum angle rotated by the rod after the collision is ( 60^{circ}-cos ^{-1} frac{z}{8} ) find the value of ( z ) | 11 |

252 | Q Type your question ( left(sigma_{1}>sigma_{2}right) ) are placed near each other separated by distance ‘d. A small change ‘ ( q ) ‘ is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at an angle of ( 45^{circ} ) with the horizontal towards plate having charge density ( sigma_{2} ) by distance ‘ ( a^{prime}(a< ) ( <boldsymbol{d}) . ) Find the work done by electric field in the process. A ( cdot frac{q aleft(sigma_{1}-sigma_{2}right)}{5 sqrt{2} epsilon_{0}} ) B. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{2 sqrt{2} epsilon_{0}} ) c. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{3 sqrt{2} epsilon_{0}} ) D. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{4 sqrt{2} epsilon_{0}} ) | 11 |

253 | A bullet of mass ( m ) and charge ( q ) is fired towards a solid uniformly charged sphere of radius ( R ) and total charge ( +q ) If it strikes the surface of the sphere with speed ( u ), find the minimum speed ( u ) so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces) ( A ) в. [ frac{q}{sqrt{4 pi varepsilon_{0} m R}} ] c. ( frac{q}{sqrt{8 pi varepsilon_{0} m R}} ) D. | 11 |

254 | A uniform rod of length ( L ) rests on a frictionless horizontal surface. The rodd is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed ( v ) strikes the rod at its centre and becomes embedded in it. The mass of the bullet is one-sixth the mass of the rod. What is the final angular velocity of the rod? A ( cdot omega=frac{v}{9 L} ) B. ( omega=frac{2 v}{9 L} ) ( c cdot omega=frac{3 v}{9 L} ) D. ( omega=frac{5 v}{9 L} ) | 11 |

255 | Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed ( v ) toward ball 2 which is at rest. Immediately after collision, ball 1 travels at a speed of ( v / 3 ) in the same direction. What type of collision has occured? A. inelastic B. elastic c. completely inelastic D. cannot be determined from the information giver | 11 |

256 | If the work done in blowing a soap bubble of volume ( ^{prime} V^{prime} ) is ( W ), then the work done in blowing is soap bubble of volume ( ^{prime} 2 V^{prime} ) is A ( .4 W ) B. ( 8 W ) ( mathbf{c} cdot 2^{1 / 3} W ) ( mathbf{D} cdot 4^{1 / 3} W ) | 11 |

257 | A rubber ball drops from a height h. If the ball rises to h / 2 after rebounding three times coefficient of restitution ( e ) is A ( cdot frac{1}{2} ) в. ( quadleft(frac{1}{2}right)^{frac{1}{2}} ) c. ( quadleft(frac{1}{2}right)^{frac{1}{4}} ) D. | 11 |

258 | A body of mass ‘ ( m^{prime} ) starting from is acted on by a force producing a velocity ( v=sqrt{k times s} ) where ( k ) is a constant and ( s ) is displacement.The work done by the force in the first ( ^{prime} t^{prime} ) seconds is: ( mathbf{A} cdot m^{2} k^{2} t^{2} / 8 ) B ( cdot m k^{2} t^{2} / 4 ) ( mathbf{c} cdot m k^{2} t^{2} / 8 ) D. ( m^{2} k^{2} t / 4 ) | 11 |

259 | A bullet of mass ( 0.01 mathrm{kg} ) is fired from a gun of mass ( 5 mathrm{kg} ) with velocity of ( 250 mathrm{m} / mathrm{s} ) calculate the speed with which the gun recoils. A. ( 0.50 mathrm{m} / mathrm{s} ) B. ( 0.25 mathrm{m} / mathrm{s} ) c. ( 0.05 mathrm{m} / mathrm{s} ) D. ( 0.025 mathrm{m} / mathrm{s} ) | 11 |

260 | A ball hits the ground and loses ( 20 % ) of its momentum. Coefficient of restitution is A. 0.2 B. 0.4 ( c cdot 0.6 ) D. 0.8 | 11 |

261 | A body of mass ( 2 mathrm{kg} ) makes an elastic collision with another body at rest and continues to move in the original direction at a speed equal to ( 1 / 3 ) of its original speed. The mass of the second body is A. ( 2 k g ) в. ( 3 k g ) c. ( 1 k g ) D. ( 4 k g ) | 11 |

262 | State work energy theorem. | 11 |

263 | The force exerted by a weird, stretch cord at given displacements is shown in the above table. Experimentally the force is found to vary proportionally to the square of the displacement, i.e. ( boldsymbol{F}(boldsymbol{x})=-boldsymbol{h} boldsymbol{x}^{2} ) where ( h ) is some constant. If the potential energy at ( x=0 m ) is ( U_{0}=0 J ) as shown above, determine the potential energy at ( x=1.5 m ) begin{tabular}{|c|c|} hline Displacement ( x ) & Force ( F ) \ hline ( 0 mathrm{m} ) & ( 0 mathrm{N} ) \ hline ( 1 mathrm{m} ) & ( -2 mathrm{N} ) \ hline ( 2 mathrm{m} ) & ( -8 mathrm{N} ) \ hline end{tabular} ( mathbf{A} cdot 1.13 J ) B. ( 2.25 J ) c. ( 4.50 J ) D. ( 6.75 J ) E ( .7 .50 J ) | 11 |

264 | A body of mass ( 6 mathrm{kg} ) is under a force whic causes displacement in it which is given by ( s=frac{t^{2}}{4} mathrm{m}, ) where ( t ) is time. The work done by the force in 2 s is A . ( 12 J ) в. ( 9 J ) c. 6.5 D. 3 | 11 |

265 | A ball of mass m moves towards a moving wall of infinite mass with a speed ‘v’ along the normal to the wall. The speed of the wall is ‘u’ toward the ball. The speed of the ball after elastic collision with wall is A. ( u+v ) away from the wall B. ( 2 u+v ) away from the wall c. ( |u-v| ) away from the wall D. ( |v-2 u| ) away from the wall | 11 |

266 | Find ( frac{boldsymbol{r}_{mathbf{1}}}{boldsymbol{r}_{2}} ) ( mathbf{A} cdot 2^{1 / 6} ) B. ( frac{1}{2^{1 / 6}} ) ( mathbf{C} cdot 2^{1 / 12} ) D. ( 2^{-1 / 12} ) | 11 |

267 | If ( M_{e} ) is the mass of earth and ( M_{m} ) is the mass of moon ( left(M_{e}=81 M_{m}right) ). The potential energy associated with object of mass ( m ) situated at a distance ( R ) from the centre of earth and ( r ) from the centre of moon, will be : ( ^{mathbf{A}} cdot_{-G m M_{m}}left[frac{R}{81}+rright] frac{1}{R^{2}} ) в. ( -G m M_{m}left[frac{81}{r}+frac{1}{R}right] ) ( ^{mathrm{c}} cdot_{-G m M_{m}}left[frac{81}{R}+frac{1}{r}right] ) D. ( -G m M_{m}left[frac{81}{R}-frac{1}{r}right. ) | 11 |

268 | A boy throws a ball of mass ( 0.5 mathrm{kg} ) upwards with an initial speed of ( 14 mathrm{m} / mathrm{s} ) The ball reaches a maximum height of 8m. The amount of energy dissipated by air drag acting on the ball during the ascent is A . 4.9 B. 9.8 c. 0 J D. 13.8 J | 11 |

269 | One man takes 1 min to raise a box to a height of 1 metre and another man takes ( 1 / 2 ) min. to do so. The potential energy in the two cases is A. different B. same c. energy of the first is more D. energy of the second is more | 11 |

270 | A pump is used to lift ( 500 k g ) of water from a depth of ( 80 m ) in ( 10 s ) (Take ( g=10 m s^{-2} ) ). Calculate the work done by the pump. A ( cdot 16 times 10^{5} J ) В. ( 4 times 10^{5} J ) c. ( 4 times 10^{8} J ) D. ( 2 times 10^{5} J ) | 11 |

271 | A body of mass ( 5 k g ) is taken from a height of ( 5 m ) to ( 10 m . ) Find the increase in its potential energy. Take ( boldsymbol{g}= ) ( 10 m s^{-2} ) A . ( 50 J ) в. ( 150 J ) ( c .250 J ) D. ( 300 J ) | 11 |

272 | 79. A rope ladder of length L is attached to a balloon of mass M. As the man of mass m climbs the ladder into the balloon basket, the balloon comes down by a vertical distance s. Then the increase in potential energy of man divided by the increase in potential energy of balloon is Fig. 8.257 L-s d. L-S Sri L- s e | 11 |

273 | A ball is dropped from a height of ( 1 m ) The coefficient of restitution between the ground and the ball is ( 1 / 3 . ) The height to which the ball will rebound after two collisions with ground is : A. ( 9 m ) в. ( 1 / 9 m ) c. ( 1 / 81 m ) D. ( 81 m ) | 11 |

274 | In a one-dimensional collision between two particles, their relative velocity is ( bar{v}_{1} ) before the collision and ( bar{v}_{2} ) and the collision. This question has multiple correct options | 11 |

275 | A person bring a mass of ( 1 k g ) from infinite to point ( A ). Initially the mass was at rest but is moves a speed of ( 2 m / s ) as it reaches to ( A ). The workdone by the person on mass is ( -3 J ) the gravitational potential at ( boldsymbol{A} ) is A. ( -3 J / k g ) в. ( -2 J / k g ) ( mathbf{c} .-5 J / k g ) D. ( -7 J / k g ) | 11 |

276 | Assertion When there is no external force on a system, its kinetic energy must remain constant Reason When there is no external force on a system its linear momentum must remain constant. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

277 | 25. A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle 30°) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is 400 Nm. The value of d is (take g = 10 ms) Lelille ) 30° Fig. 8.229 a. 25 cm c. 62.5 cm b. 37.5 cm d. None of the above | 11 |

278 | ( A B C ) is a frictionless circular track of radius ( R ). A particle of mass ( m ) kg is released from point ( boldsymbol{P}(boldsymbol{O P}=boldsymbol{R} / mathbf{2}) ) After collision with the track, particle moves along the track, then coefficient of restitution is A . 0.5 B. 0.3 ( c .0 .2 ) D. non | 11 |

279 | During “inelastic collision ” a) There is a loss of kinetic energy. b) Some of the kinetic energy is used to deform the body. c) Some of the kinetic energy is liberated as heat. d) There is a loss of mass energy. A. Only a is true B. Only b and c are true ( c cdot a, b & c ) are true D. b, c & d are true | 11 |

280 | The change in the P.E., when a body of mass ( m ) is displaced from Earth’s surface to a vertical height equal to radius of earth ( (mathrm{g}= ) acceleration due to gravity on earth surface) is: A ( cdot frac{m g R}{2} ) в. ( frac{2 m g R}{3} ) c. ( frac{3 m g R}{4} ) D. ( frac{m g R}{3} ) | 11 |

281 | The water stored in an overhead tank possesses energy | 11 |

282 | A ball is dropped onto a floor from a height of ( 10 mathrm{m} ). If ( 20 % ) of its initial energy is lost, then the height of bounce is- ( A cdot 2 m ) B. ( 4 mathrm{m} ) ( c cdot 8 m ) D. ( 6.4 mathrm{m} ) | 11 |

283 | An open knife edge of mass ( M ) is dropped from a height ( h ) on a wooden floor. If the blade penetrates distance in to the wood, the average resistance offered by the wood to the blade is A. ( M g ) в. ( M gleft(1+frac{h}{s}right) ) c. ( operatorname{Mg}left(frac{1-h}{s}right) ) D. ( M gleft(frac{1+h}{s}right)^{ } ) | 11 |

284 | The correct relation relating the potential energy U and ( r ) between two atoms is A ( cdot U_{(r)}=frac{A}{r^{12}}+frac{B}{r^{6}} ) B. ( U_{(r)}=frac{A}{r^{12}}-frac{B}{r^{6}} ) c. ( U_{(r)}=frac{A}{r^{6}}-frac{B}{r^{12}} ) D. ( -U_{(r)}=frac{K}{r^{2}} ) | 11 |

285 | A stone is dropped from a height equal to ( n R(R ) is the radius of the Earth) from the surface of the Earth. The velocity of the stone on reaching the surface of the Earth is : A ( cdot sqrt{frac{2 g(n+1) R}{n}} ) в. ( sqrt{frac{2 g R}{n+1}} ) c. ( sqrt{frac{2 g n R}{n+1}} ) D. ( sqrt{2 g n R} ) | 11 |

286 | A ball of mass m collides head on with another ball at rest. The KE of the system left is ( 50 % ). Find the coefficient of restitution. A ( cdot frac{1}{sqrt{2}} ) B. ( frac{sqrt{2}}{3} ) ( c cdot frac{1}{2} ) D. zero | 11 |

287 | Particle 1 experiences a perfectly elastic collision with a stationary particle 2. Determine their mass ratio, if after a head-on collision the particles fly apart in the opposite directions with equal velocities. A ( cdot frac{2}{3} ) B. ( frac{3}{2} ) ( c cdot frac{1}{3} ) D. 3 | 11 |

288 | A particle of mass ( m ) moving with a velocity ( (3 hat{hat{i}}+2 hat{j}) m s^{-1} ) collides with stationary body of mass ( M ) and finally moves with a velocity ( (-2 hat{i}+hat{j}) m s^{-1} ) If ( frac{M}{m}=frac{1}{13}, ) then: A ( cdot ) the impuse received by ( M ) is ( m(5 hat{i}+hat{j}) ) B. The velocity of the ( M ) is ( frac{1}{13}(5 hat{i}+hat{j}) ) c. the coefficient of restitutions ( frac{11}{17} ) D. All of the above are correct | 11 |

289 | A cosmic body ( A ) moves to the Sun with velocity ( v_{0} ) (when far from the Sun) and aiming parameter ( l ) the arm of the vector ( vec{v}_{0} ) relative to the centre of the Sun (figure shown above). Find the minimum distance by which this body will get to the Sun. | 11 |

290 | A body of mass ( 10 mathrm{kg} ) dropped from a height ( 20 mathrm{m}, ) acquires a velocity of 10 ( mathrm{m} / mathrm{s} ) after falling through a distance of 20 ( mathrm{m} ). What is the work done by the air resistance on the body? A. 750 J B. 1000 c. 1500 D. 2000 J | 11 |

291 | A sphere of mass m moving with velocity u h its another stationary sphere of same mass. If e is the coefficient of restitution, what is the ratio of velocities of two spheres after the collision? A ( .1: e ) в. ( frac{1-e}{1+e} ) c. ( frac{1+e}{1-e} ) D. ( 1: e^{2} ) | 11 |

292 | A bullet loses ( frac{1}{20} ) of its velocity after penetrating a plank. How many planks are required to stop the bullet? ( mathbf{A} cdot mathbf{9} ) B. 11 ( c cdot 7 ) D. | 11 |

293 | A block of mass ( m ) is connected to another block of mass ( M ) by a spring (massless) of spring constant ( k . ) The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force ( boldsymbol{F} ) starts acting on the block of mass ( M ) to pull it. Find the force on the block of mass ( m ) ( A cdot frac{m F}{M} ) в. ( frac{(M+m) F}{m} ) c. ( frac{m F}{(m+M)} ) D. ( frac{M F}{(m+M)} ) | 11 |

294 | A body is constrained to move in the ( y ) direction. It is subjected to a force ( (-2 hat{i}+15 hat{j}+6 hat{k}) ) Newton. The work done by this force in moving the body through a distance of ( 10 mathrm{m} ) in positive ( y ) direction is: A. 150 B. 60 J ( c ldots-20 J ) D . – 150 J | 11 |

295 | How much work they do in just holding it ? A. 250 J B. 2500 J c. 0 J D. 625 J | 11 |

296 | The angle between two vectors ( vec{A}= ) ( 4 hat{i}+3 hat{j}-2 hat{k} ) and ( vec{B}=-8 hat{i}-6 hat{j}+4 hat{k} ) is ( mathbf{A} cdot pi / 4 ) в. ( pi / 3 ) ( c ) D. ( pi / 2 ) | 11 |

297 | If K.E. of a particle increases by ( 125 % ) then what is the ( % ) increase in its momentum? | 11 |

298 | Assuming that ( m ll M, ) find at what distance ( x ) from the upper end of the rod the bullet must strike for the momentum of the system “bullet-rod” to remain constant during the impact. A ( cdot x approx frac{1}{3} l ) в. ( x approx frac{4}{3} l ) c. ( _{x} approx frac{4}{5} l ) D. ( _{x} approx frac{2}{3} l ) | 11 |

299 | Calculate the change in the gravitational potential energy of the skier between ( A ) and ( B ) : A ( cdot 1.8 times 10^{4} J ) B . ( 3.6 times 10^{2} J ) c. ( 3.6 times 10^{4} J ) D ( .1 .8 times 10^{2} J ) | 11 |

300 | A metal ball falls from a height of ( 1 mathrm{m} ) on to a steel plate and jumps upto a height of ( 81 mathrm{cm} . ) Find the coefficient of restitution of the ball material. A. 0.2 B. 9 ( c cdot 0.9 ) D. 90 | 11 |

301 | The magnitude of scalar product of two vectors is 8 and of vector product is ( 8 sqrt{3} . ) The angle between them is This question has multiple correct options A. 30 B. ( 60^{circ} ) ( c .120 ) D. 150 | 11 |

302 | The free-body diagram will be identical to the one we drew in the example of the frictionless plane, except we will have a vector for the force of friction in the negative ( x ) direction. What is the work done on the box by the force of kinetic friction? A ( . ) mumgh ( sin 30^{circ} ) B. ( mu ) mgh tan30 ( ^{text {0 }} ) c. ( mu m g h cot 30^{circ} ) D. ( mu ) mgh ( cos 30^{circ} ) | 11 |

303 | Q Type your question having track,is ( mathrm{M}=1 mathrm{kg} ) and rests over a smooth horizontal floor.A cylinder of radius ( r=10 mathrm{cm} ) and mass ( mathrm{m}=0.5 mathrm{kg} ) is hanging by thread such that axes of cylinder and track are in same level and surface of cylinder is in contact with the track as shown in figure.When the thread is burnt, cylinder starts to move down the track.Sufficient friction exists between surface of cylinder and track so that cylinder does not slip. Calculate velocity of axis of cylinder and velocity of the block when it reaches bottom of the track.Also find force applied by block on the floor at that moment. ( (g=10 ) ( left.boldsymbol{m} / boldsymbol{s}^{2}rightrangle ) | 11 |

304 | Illustration 8.34 A uniform rod of mass M and length Lis held vertically upright on a horizontal surface as shown in Fig. 8.72. Assuming zero potential energy at the base of the rod, determine the potential energy of the rod. MI Fig. 8.72 | 11 |

305 | 16. A block is suspended by an ideal spring of force constant k. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is d, then a. 7 / < 8 = 2 b. 8 = 2F k c. Work done by force F is equal to F8 d. Increase in energy stored in the spring is – ks? 2 | 11 |

306 | A particle of mass ( 5 mathrm{kg} ) is free to slide on a smooth ring of radius ( r=20 mathrm{cm} ) fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point 0 of the ring. Initially the particle is at rest at a point ( A ) of the ring such that ( angle O C A ) ( =60^{circ}, mathrm{C} ) being the centre of the ring. The natural length of the spring is also equal to ( r=20 mathrm{cm} . ) After the particle is released, it slides down the ring, the contact force between the particle ( & ) the ring becomes zero when it reaches the lowest position B. Determine the force constant of the spring. | 11 |

307 | If ( hat{i}, hat{j} ) and ( hat{k} ) represent unit vectors along the ( x, y ) and ( z ) -axes respectively, then the angle ( theta ) between the vectors ( (hat{i}+hat{j}+hat{k}) ) and ( (hat{mathbf{i}}+hat{mathbf{j}}) ) is equal to: A ( cdot sin ^{-1}left(frac{1}{sqrt{3}}right) ) B. ( sin ^{-1}(sqrt{frac{2}{3}}) ) c. ( cos ^{-1}left(frac{1}{sqrt{3}}right) ) D. ( 90^{circ} ) | 11 |

308 | U. TINC UI Wese 67. A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the kinetic energy of a projectile (KE) versus its horizontal displacement (x)? KEA DECKE b. ΚΕ KE | 11 |

309 | Two point mass ( m_{1} ) and ( m_{2} ) are placed at point ( A ) and ( B ) respectively as shown in figure.Point A is the centre of hollow sphere of uniformly distributed total mass ( m_{3} . ) Consider only gravitational interaction between all masses and neglect other gravitational forces. Select the incorrect alternative. A . Hollow sphere and point mass ( m_{1} ) moves with same acceleration B. ( m_{1} ) and ( m_{2} ) moves with same acceleration C. Net force on ( m_{1} ) is non-zero D. Net force on hollow sphere and point mass ( m_{1} ) as a system is equal to force experienced by point mass ( m_{2} ) in magnitude | 11 |

310 | A solid rectangular block of mass ( 200 k g ) has the dimensions ( l=2 m, b= ) ( 1 m, h=0.5 m . ) It lies on a horizontal floor on sides ( l ) and ( b ). The minimum work needed to turn it so that it lies on the sides ( b ) and ( h ) is: A . zero B. ( 1500 J ) c. ( 3000 J ) D. ( 2000 J ) | 11 |

311 | A cyclist comes to skidding stop in ( 10 mathrm{m} ) During this process, the force on the cycle due to the road is ( 200 mathrm{N} ) and is directly opposed to the motion.(a) how much work does the road do on the cycle? (b) How much work does the cycle do on the road? A. -2000,,20000 B. – 2000 J,1000 J by each tyre c. 0.2000 D . -2000 J,0 J | 11 |

312 | The ( X ) and ( Y ) components of a displacement vector are (15,7)( m ). Find the magnitude and direction of ( vec{A} ) | 11 |

313 | Choose the false statement A. In a perfect elastic collision, the relative velocity of approach is equal to the relative velocity of separation B. In an inelastic collision the relative velocity of approach is less than the relative velocity of separation C. In an inelastic collision, the relative velocity of separation is less than the relative velocity of approach D. In perfect inelastic collision relative velocity of separation is zero | 11 |

314 | A ball of mass ( 0.20 mathrm{kg} ) falls freely from a certain height and rebounds elastically with a speed of ( 40 mathrm{ms}^{-1} . ) The change in momentum of the ball is: A ( cdot 4 k g m s^{-1} ) B. ( 8 mathrm{kg} mathrm{ms}^{-1} ) c. ( 16 k g m s^{-1} ) D. ( 40 mathrm{kg} mathrm{ms}^{-1} ) | 11 |

315 | Using dimensional anaysis,shown that the kinetic energy of a body of mass ( mathrm{m} ) moving with a velocity v varies as ( m v^{2} ) | 11 |

316 | 44. A man places a chain (of mass m and length 1) on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length 1/2. Work done by the man in this process is a. -mg b. mg/ -3mgl d. _ mg/ 8 | 11 |

317 | Which of the following statements is true for collisions- A. Momentum is conserved in elastic collisions but not in inelastic collisions B. Total kinetic energy is conserved in elastic collisions but momentum is not conserved C. Total kinetic energy is not conserved in inelastic collisions but momentum is conserved D. Total kinetic energy and momentum both are conserved in all types of collisions | 11 |

318 | A certain simple harmonic vibrator of mass ( 0.1 k g ) has a total energy of ( 10 J ) .Its displacement from the mean position is ( 1 mathrm{cm} ) when it has equal kinetic and potential energies. The amplitude ( A ) and frequency ( n ) of vibration of the vibrator are ( ^{mathbf{A}} cdot A=sqrt{2} c m, n=frac{500}{pi} H z ) B. ( A=sqrt{2} c m, n=frac{1000}{pi} H z ) ( ^{mathbf{C}} cdot A=frac{1}{sqrt{2}} c m, n=frac{500}{pi} H z ) D. ( A=frac{1}{sqrt{2}} c m, n=frac{1000}{pi} H z ) | 11 |

319 | Two vectors ( vec{A} ) and ( vec{B} ) such that ( (vec{A}+ ) ( vec{B}) perp(vec{A}-vec{B}) . ) Then ( mathbf{A} cdot vec{A} | vec{B} ) B. ( vec{A} perp vec{B} ) C ( cdot|vec{A}|=|vec{B}| ) D ( cdot|vec{A}| neq|vec{B}| ) | 11 |

320 | A potential energy function for a twodimensional force is of the form ( U= ) ( 3 x^{2} y-7 x . ) Find the force that acts at the point ( (x, y) ) | 11 |

321 | 9. A particle is released one by one from the top of two inclined rough surfaces of height h each. The angles of inclination of the two planes are 30 and 60°, respectively. All other factors (e.g., coefficient of friction, mass of block, etc.) are same in both the cases. Let K, and K2 be the kinetic energies of the particle at the bottom of the plane in the two cases. Then a. K = K2 b. Ki > K2 c. Ki <K2 d. Data insufficient | 11 |

322 | A shell of mass ( 200 g m ) is ejected from a gun of mass ( 4 k g ) by an explosion that generates ( 1.05 k J ) of energy. The initial velocity of the shell is: A ( cdot 40 mathrm{ms}^{-1} ) B . ( 120 mathrm{ms}^{-1} ) c. ( 100 mathrm{ms}^{-1} ) D. ( 80 mathrm{ms}^{-1} ) | 11 |

323 | The figure shown a ball striking the floor at an angle ( alpha ) with speed ( u ) and rebounds at an angle ( beta ) from the floor with speed ( v . ) The value of co-efficient of restitution (e) is A ( cdot frac{v}{u} ) в. ( frac{u}{v} ) c. ( frac{v sin beta}{u sin alpha} ) D. ( frac{v sin beta}{u cos alpha} ) | 11 |

324 | A particle of rest mass ( m_{0} ) moves with a speed ( frac{C}{2} ) its total energy and kinetic energy are: ( ^{mathrm{A}} cdot frac{sqrt{3}}{2} m_{0} C^{2} ; frac{sqrt{3}}{2} m_{0} C ) в. ( frac{2}{sqrt{3}} m_{0} C^{2} ; frac{0.25}{sqrt{3}} m_{0} C^{2} ) c. ( frac{2}{sqrt{3}} m_{0} C^{2} ; frac{0.27}{sqrt{3}} m_{0} C^{2} ) D. None of these | 11 |

325 | A spring of spring constant k placed horizontally on a rough horizontal surface is compressed against a block of mass ( mathrm{m} ) placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between the block and the surface is ( mu, ) the potential energy stored in the spring is: A ( cdot frac{mu^{2} m^{2} g^{2}}{k} ) B. ( frac{2 mu^{2} g^{2}}{k} ) ( ^{mathrm{C}} cdot frac{mu^{2} m^{2} g^{2}}{2 k} ) D. ( frac{3 mu^{2} m g^{2}}{k} ) | 11 |

326 | The expression for kinetic energy is : A ( cdot frac{1}{2} m v ) в. ( frac{1}{3} m v^{2} ) c. ( frac{1}{2 m} v^{2} ) D. ( frac{1}{2} m v^{2} ) | 11 |

327 | Consider the Earth to be a homogenous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The gravitation field measured by A. A goes on decreasing and that by B goes on increasing B. B goes a decreasing and that by A goes on increasing c. each remains unchanged D. each goes on decreasing | 11 |

328 | A body of mass ( 15 mathrm{kg} ) is raised from certain depth. If the work done in raising it by ( 10 mathrm{m} ) is ( 1620 mathrm{J} ), its velocity at this position is ( mathbf{A} cdot 2 m s^{-1} ) B. ( 4 m s^{-1} ) ( mathrm{c} cdot 1 mathrm{ms}^{-1} ) D. ( 8 m s^{-1} ) | 11 |

329 | Assertion In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason In an elastic collision, the linear momentum of the system is conserved. A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement- B. Statement-1 is True, Statement-2 is True; Statement 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 | 11 |

330 | When the momentum of a body decreases by ( 10 % ), its ( mathrm{K.E.} ) decreases by A . 20% B. 40% c. 36% D. None of these | 11 |

331 | A cannon, shell is fired to hit a target at a horizontal distance ( boldsymbol{R} ). However, it breaks into two equal parts at its highest point. One part (A) returns to the cannon. The other part: This question has multiple correct options A. will fall at a distance of ( R ) beyond the target B. will fall at a distance of ( 3 R ) beyond the target c. will hit the target D. have nine times the kinetic energy of ( A ) | 11 |

332 | Two bodies of equal weight are kept at heights of ( h ) and ( 1.5 h ) respectively. The ratio of their P.E. is ( A cdot 3: 2 ) B. 2:3 ( c cdot 1: 1 ) D. None of these | 11 |

333 | A thin circular ring of mass ( M ) and radius ‘ ( r^{prime} ) is rotating about its axis with a constant angular velocity ( omega . ) Four object each of mass ( m, ) are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be- | 11 |

334 | The potential energy of an object of mass ( m ) moving in ( x y ) plane in a conservative field is given by ( boldsymbol{u}=boldsymbol{a} boldsymbol{x}+ ) ( b y, ) where ( x ) and ( y ) are position coordinates of the object. Find magnitude of its acceleration. | 11 |

335 | Work done on body equals to change in its kinetic energy is known as A. work done principle. B. work-energy principle. c. work-velocity principle. D. speed-displacement principle | 11 |

336 | A father holds his child on his shoulders during a parade. The father does no work during the parade because: A. No force acts on the child B. The momentum of the child is constant c. The potential energy of the child is varying D. The child’s kinetic energy is constant E. The child’s distance from the gro | 11 |

337 | What is the magnitude of linear velocity of the stick plus puck after the collision? ( mathbf{A} cdot v_{i} ) B. ( frac{v_{i}}{3} ) ( c cdot frac{v_{i}}{2} ) D. ( frac{v_{i}}{sqrt{2}} ) | 11 |

338 | When the bob of a simple pendulum is displaced to one extreme position ( mathrm{P} ) and then released, it swings towards the centre position ( Q ) and then to the other extreme position R. At which position does the bob have maximum kinetic energy? A. Between P and Q B. ( c cdot R ) D. Between Q and R | 11 |

339 | Show that the total kinetic energy of a sphere of mass ( m ) rolling along horizontal plane with velocity ( boldsymbol{v} ) is ( 7 / 10 m v^{2} ) | 11 |

340 | A neutron moving with a speed ( v ) makes a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place is A . ( 10.2 e V ) B. 20.4eV c. ( 12.1 e V ) D. ( 16.8 e V ) | 11 |

341 | A body is acted upon by force which is inversely proportional to the distance covered. The work done will be proportional to: ( A ) B ( cdot s^{2} ) c. ( sqrt{s} ) D. None of the above | 11 |

342 | The sum of magnitudes of two forces acting at a point is ( 16 N . ) If the resultant force is ( 8 N ) and its direction is perpendicular to smaller force, then the forces are: A 6 Nand ( 10 N ) n B. ( 8 N ) and ( 8 / N ) c. ( 4 N ) and ( 12 N ) D. ( 2 N ) and ( 14 N ) | 11 |

343 | In the figure shown, a block A moving with velocity ( 10 ~ m / s ) on a horizontal surface collides with another block B at rest initially. The coefficient of restitution is ( frac{1}{2} . ) Neglect friction everywhere. The distance between the blocks at ( 5 s ) after the collision takes place is ( 5 x(text { in } m) . ) Then ( x ) is | 11 |

344 | Assertion A particle is projected upwards with speed ( v ) and it goes to a height ( h . ) If we double the speed then it will move to height ( 4 h ) Reason In case of earth, acceleration due to gravity ( g ) varies as ( g propto frac{1}{r^{2}} r geq R ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

345 | A block strikes the free end of a horizontal spring with the other end fix, placed on a smooth surface with a speed ( v . ) After compressing the spring by ( x, ) the speed of the block reduce to half. Calculate the maximum compression of the spring. | 11 |

346 | If the vectors ( vec{P}=a tilde{i}+a hat{j}+ ) 3 ( hat{k} ) and ( vec{Q}=a hat{i}-2 hat{j}-hat{k} ) are perpendicular to each other then the positive value of a is A . zero в. ( c cdot 2 ) D. 3 | 11 |

347 | Can you find at least one vector perpendicular to ( 3 hat{i}-4 hat{j}+7 hat{k} ? ) A ( cdot hat{i}+2 hat{j}+frac{6}{7} hat{k} ) B・ ( _{hat{i}+2 hat{j}}+frac{5}{7} hat{k} ) ( mathbf{c} cdot hat{i}+3 hat{j}+frac{5}{7} hat{k} ) D・ ( hat{i}+2 hat{j}+frac{5}{6} hat{k} ) | 11 |

348 | A block of mass ( 100 g ) is moved with a speed of ( 5.0 m / s ) at the highest point in a closed circular tube of radius tube of radius ( 10 mathrm{cm} ) kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process. A. ( -1.45 mathrm{J} ) в. +1.45 J c. ( -2.9 J ) D. ( +2.9 J ) | 11 |

349 | A disc of radius ( 0.1 ~ m ) rolls without sliding on a horizontal surface with a velocity of ( 6 m / s^{-1} ). Then, it ascends a smooth continuous track as shown in the figure. Given, ( g=10 m s^{-1}, ) the height up to which it will ascend is ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) A ( .2 .4 n ) в. 0.9 т ( c .2 .7 m ) D. ( 1.8 mathrm{m} ) | 11 |

350 | Tllustration 8.21 A bullet leaving the muzzle of a rifle barrel with a velocity v penetrates a plank and loses one-fifth of its velocity. It then strikes second plank, which it just penetrates through. Find the ratio of the thickness of the planks, supposing the average resistance to the penetration is same in both the cases. | 11 |

351 | Which of the following are correct? This question has multiple correct options A. An astronaut going from the earth to the Moon will experience weightlessness once. B. When a thin uniform spherical shell gradually shrinks maintaining its shape, the gravitational potential at its centre decreases C. In the case of a spherical shell, the plot of ( V ) versus ( r ) is continuous. D. In the case of a spherical shell, the plot gravitational field intensity ( I ) versus ( r ) is continuous | 11 |

352 | toppr Q Type your question uniform area of cross-section is attached with the particle. The other end of the band is suspended from a rigid support. A force ( boldsymbol{K}left(boldsymbol{l}^{prime 2}-boldsymbol{l}^{2}right)^{1 / 2} ) is required to stretch the band to a length ( l^{prime} . ) The particle is moved to a distance ( S ) (where ( S<<l ) ) and then released. taking ( K=frac{M g}{S} ) and ( mu ) as the coefficient of friction between the particle and the groove, the velocity of particle when passing through the initial position is: ( ^{A} cdotleft(frac{g S}{3 l}(2 S-3 mu l)right)^{1 / 2} ) B. ( left[frac{g S}{3 l}(3 S-3 mu l)^{1 / 2}right] ) c. ( frac{g S}{l}(3 S-2 mu l)^{1 / 2} ) ( ^{mathrm{D}}left[frac{g S}{2 l}(3 S-2 mu l)right]^{1 / 2} ) | 11 |

353 | If two balls each of mass ( 0.06 mathrm{Kg} ) moving in opposite directions with speed ( 4 mathrm{m} / mathrm{sec} ) collides and rebound with the same speed,then coefficient of restitution for the collision will be:- ( A cdot frac{1}{4} ) B. ( c ) D. | 11 |

354 | The maximum extension of the spring ( boldsymbol{x}_{boldsymbol{m}} ) is ( A cdot frac{m g}{K} ) в. ( frac{2 m g}{K} ) c. ( frac{3 m g}{K} ) D. ( frac{4 m g}{K} ) | 11 |

355 | A small body ( A ) starts sliding off the top of a smooth sphere of radius ( R ). Find the angle ( theta ) (shown in figure above) corresponding to the point at which the body breaks off the sphere as well as the break-off velocity of the body A ( quad theta=arccos left(frac{1}{3}right) approx 52^{circ}, v=sqrt{frac{2 g R}{3}} ) B. ( theta=arccos left(frac{2}{3}right) approx 48^{circ}, v=sqrt{frac{2 g R}{3}} ) ( ^{mathrm{c}} cdot_{theta}=arccos left(frac{2}{3}right) approx 48^{circ}, v=sqrt{frac{g R}{3}} ) D. ( _{theta}=arccos left(frac{1}{3}right) approx 52^{circ}, v=sqrt{frac{g R}{3}} ) | 11 |

356 | 12. A block hangs freely from the end of a spring. A boy then slowly pushes the block upwards so that the spring becomes strain free. The gain in gravitational potential energy of the block during this process is not equal to a. The work done by the boy against the gravitational force acting on the block b. The loss of energy stored in the spring minus the work done by the tension in the spring c. The work done on the block by the boy plus the loss of energy stored in the spring d. The work done on the block by the boy minus the work done by the tension in the spring plus the loss of energy stored in the spring e. The work done on the block by the boy minus the work done by the tension in the spring | 11 |

357 | A body of mass ( 1.5 mathrm{kg} ) is allowed to slide down along a quadrant of a circle from the horizontal position. In reaching to the bottom, Its velocity is ( 8 mathrm{m} / mathrm{s} ). The work done in overcoming the friction is 12J. The radius of circle is | 11 |

358 | A cord is used to lower vertically a block of mass ( M ) by a distance ( d ) with constant downword acceleration ( frac{g}{2} ) work done by the cord on the block is ( ^{mathbf{A}} cdot frac{-M g d}{2} ) B. ( frac{M g d}{4} ) c. ( frac{-3 M g d}{4} ) D. ( M g d ) | 11 |

359 | 3. Which of the following energies is conserved for the system? a. Kinetic energy b. Potential energy c. Mechanical energy d. None of these | 11 |

360 | 19. A constant force F pushes the block m till the wedge M starts sliding. If the stiffness of the light spring connecting M and m is K, coefficient of friction between block and wedge is y, and between the wedge and ground is My, find the value of the force F pornoon м | Fig. 8.222 | 11 |

361 | A body moving towards a finite body at rest collides with it. It is possible that: This question has multiple correct options A. both the bodies come to rest B. both the bodies moves after collision C. the moving body comes to rest and the stationary body starts moving D. the stationary body remains stationary, the moving body changes its velocity | 11 |

362 | A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is ( 50 mathrm{m} ) where ( mathrm{m} ) is the mass of the one shell. If the muzzle velocity of shell is ( 200 mathrm{m} / mathrm{s} ), what is recoil speed of car after second shot? A ( cdot frac{200}{49} mathrm{m} / mathrm{s} ) в. ( 200left(frac{1}{48}+frac{1}{48}right) mathrm{m} / mathrm{s} ) ( ^{mathrm{c}} cdot_{200}left(frac{1}{48}+frac{1}{49}right) mathrm{m} / mathrm{s} ) D. ( 200left(frac{1}{48}+frac{1}{48 times 49}right) mathrm{m} / mathrm{s} ) | 11 |

363 | The two masses ( m_{1} ) and ( m_{2} ) are joined by a spring as shown. The system is dropped to the ground from a height. The spring will be A. neither compressed nor stretched regardless of the value of ( m_{1} ) and ( m_{2} ) B. neither compressed nor stretched only when ( m_{1}=m_{2} ) c. stretched when ( m_{2}>m_{1} ) D. compressed when ( m_{2}<m_{1} ) | 11 |

364 | Two elastic bodies ( P ) and ( Q ) having equal masses are moving along the same line with velocities of ( 16 mathrm{m} / mathrm{s} ) and ( 10 mathrm{m} / mathrm{s} ) respectively. Their velocities after the elastic collision will be in ( mathrm{m} / mathrm{s} ) A. 0 and 25 B. 5 and 20 c. 10 and 16 D. 20 and 5 | 11 |

365 | A block of mass ( m=0.1 mathrm{kg} ) is released from a height of ( 4 mathrm{m} ) a curved smooth surface. On the horizontal surface path AB is smooth and path BC offers coefficient of friction ( mu=0.1 . ) If the impact of block with vertical wall at ( C ) be perfectly elastic, find the total distance covered by the block on the horizontal surface before coming to rest. (Take ( left.mathfrak{g}=10 frac{m}{s^{2}}right) ) | 11 |

366 | 12. An engine pumps water continuously through a hole. Speed with which water passes through the hole nozzle is v, and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water. a. I kv2 b. 1 kv? c. 2 d. v 2 2k 2k anned by applying a catarina face when | 11 |

367 | Two identical balls ( A & 13 ) of mass ( m ) each are placed on a fixed wedge as shown in figure Ball B is kept at rest and it is released just before two balls collides. Bali A roll down without slipping on inclined plane ( & ) collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is: A ( cdot frac{m g h}{7} ) B. ( frac{m g h}{2} ) c. ( frac{2 m g h}{5} ) D. ( frac{7 m g h}{5} ) | 11 |

368 | Q Type your question. smooth pulley as shown in figure. If the system is released from rest, find the work done by tension on both ( 1 mathrm{kg} ) and 2 kg blocks in 1 s. (Take ( g=10 m / s^{2} ) ) A ( cdot frac{200}{9} J,-frac{200}{9} J ) В. ( -frac{200}{9} J,+frac{200}{9} J ) c. ( +frac{200}{9} J,+frac{200}{9} J ) | 11 |

369 | A sphere of mass ( m_{1}=2 k g ) collides with a sphere of mass ( m_{2}=3 k g ) which is at rest. Mass ( m_{1} ) will move at right angle to the line joining centres at the time of collision, if the coefficient of restitution is A ( cdot frac{4}{9} ) в. ( frac{1}{2} ) ( c cdot frac{2}{3} ) D. ( sqrt{frac{2}{3}} ) | 11 |

370 | The K.E. of a body is increased most by doubling its : A. mass B. weigth c. speed D. P.E | 11 |

371 | An automobile spring extends ( 0.2 mathrm{m} ) for ( 5000 mathrm{N} ) load. The ratio of potential energy stored in this spring when it has been compressed by ( 0.2 mathrm{m} ) to the potential energy stored in a ( 10 mathrm{F} ) capacitor at a potential difference of ( 10000 mathrm{V} ) will be: A ( cdot 1 / 4 ) B. ( c cdot 1 / 2 ) ( D cdot 2 ) | 11 |

372 | Two men, each of mass ( m ), stand on the edge of a stationary car and jump off with a horizontal velocity u relative to the car, first simultaneously and then one after the other. If friction be negligible, in which case will they impart greater speed to the car? | 11 |

373 | Which of the following energy change involves frictional force? A. Chemical energy to heat energy B. Kinetic energy to heat energy C. Potential energy to sound energy D. chemical energy to kinetic energy | 11 |

374 | State whether the given statement is True or False : A block of mass ( M ) is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force ( boldsymbol{F} ). The kinetic | 11 |

375 | A small particle travelling with a velocity v collides elastically with a smooth spherical body of equal mass and of radius ( r ) initially kept at rest. The centre of this spherical body is located a distance 8 | 11 |

376 | What is the least amount of energy required by a man to lift an object weighing ( 1000 mathrm{N} ) to a height of ( 2 m ? ) A. 500 J B. 2000 N c. ( 500 mathrm{N} ) D. 2000 J | 11 |

377 | 9. A man M, of mass 80 kg runs up a staircase in 15 s. Another man M, also of mass 80 kg runs up the same staircase in 20 s. The ratio of the powers developed by them will be a. 1 d. none of these | 11 |

378 | Two block ( A ) and ( B ) are connected to each other as shown is fig. and spring and pulley. The block ( B ) slides at a horizontal top surface of stationary block ( C, ) and block ( A ) slides along vertical slides of ( C ), both with same uniform speed. The coefficient of friction between the block is ( 0.2(l) ) spring constant of spring is ( 1960 N / m ) f mass of block is ( 2 k g ). Find energy stored in spring, | 11 |

379 | Assertio A block of mass ( m ) starts moving on a rough horizontal surface with a velocity ( v . ) It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of ( 30^{circ} ) with the horizontal and the same block is made to go up on the surface with the same initial velocity ( v ). The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Reason The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

380 | Kinetic energy depends on: A. Position B. Velocity c. shape D. colour | 11 |

381 | f a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k}, ) then the value of ( alpha ) A . – B. ( -frac{1}{2} ) ( c cdot frac{1}{2} ) ( D ) | 11 |

382 | Find the total acceleration of the sphere as a function of ( boldsymbol{theta}, ) the angle of deflection of the thread from the vertical. A. ( w=g sqrt{1+2 cos ^{2} theta} ) В. ( w=g sqrt{2+3 cos ^{2} theta} ) c. ( w=g sqrt{1+3 cos ^{2} theta} ) D. ( w=g sqrt{3+2 cos ^{2} theta} ) | 11 |

383 | 24. A force F = 3î + 24 +ck N causes a displacement r = ci +4j+ck m. The work done is 36 J. Find the value(s) of c. | 11 |

384 | A stationary body explodes into two fragments of masses ( boldsymbol{m}_{1} ) and ( boldsymbol{m}_{2} . ) If momentum of one fragments ( mathrm{p} ), the minimum energy of explosion is ( ^{mathbf{A}} cdot frac{p^{2}}{2left(m_{1}+m_{2}right)} ) В. ( frac{p^{2}}{2 sqrt{m_{1} m_{2}}} ) c. ( frac{p^{2}left(m_{1}+m_{2}right)}{4 m_{1} m_{2}} ) D. ( frac{p^{2}}{2left(m_{1}-m_{2}right)} ) | 11 |

385 | Initially, the spheres ( A ) and ( B ) are the potential ( V_{A} ) and ( V_{B} ) respectively. Now sphere ( mathrm{B} ) is earthed by closing the switch. The potential of A will now become ( _{–} ) ( mathbf{A} cdot mathbf{0} ) B. ( V_{A} ) ( mathbf{c} cdot V_{A}-V_{B} ) D. ( V_{B} ) | 11 |

386 | The work-energy theorem states that the change in: A. kinetic energy of a particle is equal to the work done on it by the net force B. kinetic energy of a particle is equal to the work done by one of the forces acting on it C. potential energy of a particle is equal to the work done on it by the net force D. potential energy of a particle is equal to the work done by one of the forces acting on it E. total energy if a particle is equal to the work done on it by the net force | 11 |

387 | The electric current is produced by the stored water in dams,which possess: A. Wind Energy B. Potential Energy C. Kinetic Energy D. Solar Energy | 11 |

388 | Imagine a light planet revolving around a very massive star in a circular orbit or radius ( R ) with a speed of revolution ( T . ) If the gravitational force of attraction between the planet and the star is proportional to ( boldsymbol{R}^{-mathbf{5} / 2}, ) then A ( cdot T^{2} ) is proportional to ( R^{2} ) B . ( T^{2} ) is proportional to ( R^{7 / 2} ) c. ( T^{2} ) is proportional to ( R^{3 / 2} / 2 ) proportional D. ( T^{2} ) is proportional to ( R^{3.75} ) | 11 |

389 | Q Type your question- tative cu titteratur ac a mgin ( n_{1} ) above the floor of the elevator. After making a collision with the floor of the elevator it bounces to height ( h_{2} ). The coefficient of restitution for collision is e. For this situation, mark the correct statement(s). A . If elevator is moving down with constant velocity ( nu_{0} ) then ( h_{2}=e^{2} h_{1} ) B. If elevator is moving down with constant velocity ( nu_{0} ) then ( h_{2}=e^{2} h_{1}-frac{nu_{0}^{2}}{2 g} ) c. If elevator is moving with constant acceleration of ( g / 4 ) in upward direction, then impulse imparted by floor of the elevator to the ball is ( m(sqrt{2 g h_{2}})+sqrt{2 g h_{1}}+2 nu_{0} ) D. If elevator is moving with constant acceleration of ( g / 4 ) in upward direction, then it is not possible to determine a reaction between ( h_{1} ) and ( h_{2} ) from the given information. | 11 |

390 | ( A ) block ( A, ) whose weight is ( 200 N, ) is pulled up a slope of length ( 5 m ) by means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) ) as illustrated in the figure.The difference in work done by the force and the increase in potential energy of the block is : A . ( 0 . ) в. ( 150 J ) ( c .750 J ) D. ( 600 J ) | 11 |

391 | The amount of work has to be done in assembling three charged particles at the vertices of an equilateral triangle A .434 в. 334 c. 234 」 D. 134 J | 11 |

392 | The spring of the winding knob of a watch has A. mechanical energy B. only kinetic energy c. only potential energy D. kinetic or potential energy | 11 |

393 | rest on a inclined plane and are separated by a distance of 6.0 m as shown in figure. The coefficient of friction between each of the blocks and the inclined plane is ( 0.25 . ) The ( 2 k g ) block is given a velocity of ( 10.0 mathrm{m} / mathrm{s} ) up the inclined plane. It collides with ( boldsymbol{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 comes to rest. calculated the coefficient [Take ( sin theta= ) ( left.tan theta=0.05 text { and } g=10 m / s^{2}right] ) ( mathbf{A} cdot e=0.84, M=15 k g ) в. ( e=4, M=5 k g ) c. ( e=9, M=15 k g ) D. ( e=84, M=17 k g ) | 11 |

394 | A ball of mass M moving with a velocity V collides head on elastically with another of same mass but moving with a velocity v in the opposite direction After collision, A. the velocities are exchanged between the two balls B. both the balls come to rest c. both of them move at right angles to the original line of motion D. one ball comes to rest and another ball travels back with velocity ( 2 v ) | 11 |

395 | Energy possessed by a body by virtue of its motion is : A. Potential energy B. Kinetic energy c. Chemical energy D. Electrical energy | 11 |

396 | Calculate the work done to rise a body of ( 30 mathrm{kg} ) to a height of ( 50 mathrm{m}left(mathrm{g}=10 mathrm{m} mathrm{s}^{-2}right) ) (in kJ) A . 100 B. c. 15 D. 0.5 | 11 |

397 | The resultant of two vectors ( vec{P} ) and ( vec{Q} ) is ( vec{R} ) If ( vec{Q} ) is doubled then the new resultant vector is perpendicular to ( vec{P} ) Then magnitude of ( overrightarrow{boldsymbol{R}} ) is: ( ^{mathbf{A}} cdot frac{P^{2}-Q^{2}}{2 P Q} ) в. ( Q ) c. ( frac{P}{Q} ) D. ( frac{P+Q}{P-Q} ) | 11 |

398 | The potential energy of your body is least when you are… | 11 |

399 | 7. Mark the correct statement(s). a. Total work done by internal forces of a system on the system is always zero. b. Total work done by internal forces of a system on the system is sometimes zero. c. Total work done by internal forces acting between the particles of a rigid body is always zero. d. Total work done by internal forces acting between the particles of a rigid body is sometimes zero. par o n e.meat antitance | 11 |

400 | Example 8.9 A small bar A resting on a smooth horizontal plane is attached by threads to a point P and by means of weightless pulley, to a weight B possessing the same mass as the bar itself. The bar is also attached to a point O by means of a light non-deformed spring of length lo = 50 cm and stiffness k=mgllo, where m is the mass of the bar. The thread PA having been burned, the bar starts moving to the right. Find its velocity at the moment when it is breaking off the plane. Fig. 8.189 | 11 |

401 | A force ( overrightarrow{boldsymbol{F}}=(mathbf{5} hat{boldsymbol{i}}+boldsymbol{4} hat{boldsymbol{j}}) boldsymbol{N} ) acts on a body and produced a displacement ( overrightarrow{boldsymbol{S}}= ) ( (6 hat{i}-5 hat{j}+3 hat{k}) m . ) The work done will be A . ( 10 J ) в. 20 ( J ) ( c .30 J ) D. ( 40 J ) | 11 |

402 | A force ( overrightarrow{boldsymbol{F}}=boldsymbol{x} hat{boldsymbol{i}}+boldsymbol{2} boldsymbol{y} hat{boldsymbol{j}} ) is applied on a particle. Find out work done by ( boldsymbol{F} ) to move the particle from point ( boldsymbol{A} ) to ( boldsymbol{B} ) A . ( -3.5 ~ J ) в. ( -2.5 mathrm{J} ) c. ( -4.5 J ) D. -45 | 11 |

403 | 53. Net work done by the force F on the block is a. 50J b. – – I c. 75 J d. None of these | 11 |

404 | A body of mass ( m ) is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be A. ( 3 m g R ) B. ( frac{1}{3} m g R ) c. ( 2 m g R ) D. ( frac{2}{3} m g R ) | 11 |

405 | By how much will the kinetic energy of a body increase if its speed is doubled? A. 4 times B. 2 times c. 8 times D. 16 times | 11 |

406 | A ball is thrown vertically downwards with velocity ( sqrt{2 g h} ) from a height ( h ) After colliding with the ground it just reaches the starting point. Coefficient of restitution is : A. ( 1 / sqrt{2} ) B. ( 1 / 2 ) c. 1 D. ( sqrt{2} ) | 11 |

407 | 12. What is the mechanical energy of the system? a. 35 J b. 64 J c. 86 J d. 49 J | 11 |

408 | Two identical balls of equal masses ( A ) and ( mathrm{B} ) are lying on a smooth surface as shown in figure. Ball A hits the ball B (which is at rest) with a velocity ( mathbf{v}=16 ) ( mathrm{m} / mathrm{s} . ) What should be the minimum value of coefficient of restitution between ( A ) and ( B ) so that ( B ) just reaches the highest point of inclined plane: ( left(g=10 m / s^{2}right) ) ( A cdot frac{2}{3} ) B. ( frac{1}{2} ) ( c cdot frac{1}{3} ) D. | 11 |

409 | What kind of energy transformation takes place at the thermal power station? | 11 |

410 | A body of mass ( m ) was slowly hauled up the hill by a force ( F ) as shown in the figure, which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is ( h, ) the length of its base is ( l ) and the coefficient of friction is ( mu . ) (Given acceleration due to gravity ( =g) ) A ( . W_{F}=m g h+mu m g l ) В. ( W_{F}=m g h-mu m g l ) c. ( W_{F}=mu m g l-m g h ) 2. | 11 |

411 | A body of mass ( 10 k g ) at rest is acted upon simultaneously by two forces ( 4 N ) and ( 3 N ) at right angles to each other. The kinetic energy of the body at the end of ( 10 s ) is begin{tabular}{l} A. ( 50 mathrm{J} ) \ hline end{tabular} в. ( 100 J ) c. ( 125 J ) D. ( 144 J ) | 11 |

412 | A block of mass ( m=0.1 mathrm{kg} ) is released from a height of ( 4 mathrm{m} ) on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC offers coefficient of friction ( mu=0.1 . ) If the impact of block with the vertical wall at ( mathrm{C} ) be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be : ( left.operatorname{take} g=10 m / s^{2}right) ) A ( .29 m ) в. ( 49 m ) ( mathbf{c} .59 m ) ( mathbf{D} cdot 109 m ) | 11 |

413 | Assertion In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason In an elastic, the linear momenta of the system is conserved. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect and Reason correct | 11 |

414 | Two bodies ( A ) and ( B ) of equal masses are kept at height of h and ( 2 h ) respectively. ratio of their potential energy? | 11 |

415 | In which of the following cases work is said to be done? A. A man pushing a roller and displacing it B. A boy sleeping c. Girl writing in Examm D. All of these | 11 |

416 | 15 32. A particle of mass m is projected at an angle a to the horizontal with an initial velocity u. The work done by gravity during the time it reaches its highest point is a. u? sin’a h mu costa mu’sin’ a d mu sina c. | 11 |

417 | A boy held a book of ( 1 mathrm{kg} ) at a height of 1 metre for 60 seconds. Calculate the work done. A . 60 J B. 30 J c. 15 J D. | 11 |

418 | Find the velocity of the disc after the collision. A. ( v^{prime}=frac{4+eta}{4+eta} v ) B. ( v^{prime}=frac{4-eta}{4-eta} v ) ( ^{mathrm{C}} cdot v^{prime}=frac{4-eta}{4+eta} v ) D. ( v^{prime}=frac{4+eta}{4-eta} v ) | 11 |

419 | 17. The work done on a particle of mass m by a force alatymitatio ja being the constant K being the constant of appropriate dimensions, when the particle is taken from the point (a,0) to the point (0, a) along a circular path of radius a about the origin in the r-y plane is a 2Kx Kx Kr 2 d. o (JEE Advanced, 2013) | 11 |

420 | At what value of ( eta ) will the velocity of the disc after the collision reverse its direction? A. ( eta4 ) ( mathbf{c} cdot eta=4 ) D. ( eta=0 ) | 11 |

421 | A weight lifter jerks ( 220 k g ) vertically through 1.5meters and holds still at that height for two minutes. The work done by him in lifting and in holding it still are respectively (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s} ) ): A. ( 220 J, 330 J ) в. ( 3234 J, 0 ) c. ( 2334 J, 10 J ) D. ( 0,3234 J ) | 11 |

422 | c The displacement-time graph of a body acted upon by some es is shown in Fig. 8.291. For this situation match the entries of Column I with the entries of Column II. SA Straight Fig. 8.291 Column I Column II i. For OA, the total work done a. always positive by all forces together is ii. For OA, the work done by few b. can be positive of the acting forces is iii. For AB, the work done by few c. zero or can be of the acting forces is iv. For BC, the work done by all d. can be negative forces together is zero | 11 |

423 | Two masses ( m_{1} ) and ( m_{2} ) are connected by a spring of spring constant k and are placed on a smooth horizontal surface. Initially the spring is stretched through a distance ‘d’ when the system is released from rest. Find the distance moved by the two masses when spring is compressed by a distance ‘d’. | 11 |

424 | 24. If instead of moving up the plane, the man increases his speed to the value v while moving down the inclined plane through the same vertical distance h, then a. W friction > 0 b. W friction = -mgh + mv2 c. Work done by the man can be positive, negative or zero 2 d. Wfriction + W man = -mgh+ -mv2 | 11 |

425 | A ball is thrown horizontally from the top of a tower ( 40 mathrm{m} ) high. The ball strikes the ground at a point ( 80 mathrm{m} ) from the bottom of the tower. Find the angle that the velocity vector makes with the horizontal just before the ball hits the ground. ( mathbf{A} cdot 45 m / s ) в. ( 90 mathrm{m} / mathrm{s} ) c. ( 37 m / s ) D. ( 53 m / s ) | 11 |

426 | Which of the following pairs of vectors are parallel? A ( . vec{A}=hat{i}-2 hat{j} ; vec{B}=hat{i}-5 hat{j} ) B . ( vec{A}=hat{i}-10 hat{j} ; vec{B}=2 hat{i}-5 hat{j} ) c. ( vec{A}=hat{i}-5 hat{j} ; vec{B}=hat{i}-10 hat{j} ) D. ( vec{A}=hat{i}-5 hat{j} ; vec{B}=2 hat{i}-10 hat{j} ) | 11 |

427 | The gravitational field is a conservative field. The work done in this field by moving an object from one point to another A. depends on the end-points only. B. depends on the path along which the object is moved. C. depends on the end-points as well as the path between the points. D. is not zero when the object is brought back to its initial position. | 11 |

428 | Two blocks of masses ( M_{1} ) and ( M_{2} ) are connected by spring of constant ( boldsymbol{K} ). The spring is initially compressed and the system is released from rest at ( t=0 ) second. The work done by spring on the blocks ( M_{1} ) and ( M_{2} ) be ( W_{1} ) and ( W_{2} ) respectively by time t. The speeds of both the blocks at time t are non zero. Then the value of ( frac{W_{1}}{W_{2}} ) equals to A ( cdot frac{M_{1}}{M_{2}} ) в. ( frac{M_{2}}{M_{1}} ) ( ^{mathrm{c}}left(frac{M_{1}}{M_{2}}right)^{2} ) ( ^{mathrm{D}}left(frac{M_{2}}{M_{1}}right)^{2} ) | 11 |

429 | An electron moving in a electric potential field ( V_{1} ) enters a higher electric potential field ( V_{2} ) then the change in kinetic energy of the electron is proportional to | 11 |

430 | A sphere of mass ( mathrm{m}, ) moving with a speed ( v, ) strikes a wall elastically at an angle of incidence ( theta ). If the speed of the sphere before and after collision is the same and the angle of incidence and velocity normally towards the wall the angle of rebound is equal to the angle of incidence and velocity normally towards the wall is taken as negative then, the change in the momentum parallel to wall is : A. mv ( cos theta ) B. 2 mv ( cos theta ) c. – 2 mv ( cos theta ) D. zero | 11 |

431 | A ( 3.0 k g ) lump of clay is moving to the left at ( 4.0 m / s . ) It collides in a perfectly inelastic collision with a ( 6.0 k g ) lump of clay moving to the right at ( 2.0 m / s ) What is the total kinetic energy after the collision? ( A cdot 62 J ) в. ( 36 J ) c. ( 25 J ) D. ( 12 . J ) E . ( 0 . J ) | 11 |

432 | Name the type of energy (kinetic energy ( K ) or potential energy ( U ) ) possessed in a compressed spring: A. ( U ) в. ( K ) c. Both ( U ) and ( K ) D. None | 11 |

433 | A vibrating body possesses: A. electrical energy B. nuclear energy C . potential energy D. sound energy | 11 |

434 | A man of 60 kg gains 1000 cal of heat by eating 5 mangoes. His efficiency is ( 56 % ) To what height he canjump by using this energy? ( mathbf{A} cdot 4 m ) в. ( 20 m ) ( c .28 m ) D. ( 0.2 m ) | 11 |

435 | When a force retards the motion of a body, the work done is : A. zero B. Negative c. Positive D. Positive or negative depending upon the magnitude of force and displacement | 11 |

436 | State whether the given statement is True or False : The energy of an object that is due to the object’s motion is called kinetic | 11 |

437 | 45. Along which of the three paths is the work done maximum? а. ОА b. OMA c. OLA d. Work done has the same value for all the three paths. | 11 |

438 | A man is climbing a staircase. The energy he uses depends on: This question has multiple correct options A. The height of the staircase. B. The weight of his body c. The time taken to roach the top D. The mass of his body. | 11 |

439 | Two solid balls of rubber ( A ) and ( B ) whose masses are ( 200 g m ) and ( 400 g m ) respectively, are moving in mutually opposite directions. if the velocity of bal ( A ) is ( 0.3 m / s ) and both the ball come to rest after collision, then the velocity of ball ( B ) is : A. ( 0.15 mathrm{m} / mathrm{s} ) в. ( -0.15 mathrm{m} / mathrm{s} ) c. ( 1.5 mathrm{m} / mathrm{s} ) D. None of these | 11 |

440 | A ball of mass ( 0.2 k g ) is thrown against the wall, the ball strikes the wall normally with velocity of ( 30 m / s ) sand rebounds with velocity of ( 20 m / s ) Calculate the impulse of the force exerted by the ball on the wall A . ( 2 N ) в. ( -10 N ) ( c .20 N ) D. ( 40 N ) | 11 |

441 | toppr Q Type your question height 1 m above the ground. The particle is thrown from some point in such a way that it strikes the ground (perfectly inelastic) with velocity ( v_{0} ) at an angle ( 37^{circ} ) with vertical just below ( O ) List (P) Radius of curvature of particle just before striking the ground (Q) Minimum value of ( v_{0} ) such that at highest point in vertical circle tension in the string ( T=0 ) (R) Negative of work done by gravity after it strikes the ground to the topmost point in frame moving with constant acceleration on ground is (assume that after collision the particle complete the vertical loop) (S) Power delivered by the gravity at highest point is (assume that after [ frac{5}{3} frac{v_{0}^{2}}{g} ] collision the particle complete the vertical loop) A. P- ( 2 ; Q-3 ; R-1 ; S-4 ) B. P- 3; Q- 2; R- 4; S-1 ( mathrm{C} cdot cdot mathrm{Q}-1 ; mathrm{R}-2 ; mathrm{S}-3 ) D. P- 2; Q- 3; R-4; S-1 | 11 |

442 | A woman weighing ( 63 mathrm{kg} ) eats plum cake whose energy content is 9800 calories. If all this energy could be utilized by her, she can ascend a height of A. ( 1 m ) B. ( 66 m ) ( c cdot 100 m ) D. ( 42 m ) | 11 |

443 | Assertion Work done by friction on a body sliding down an inclined plane is negative Reason Work done is greater than zero, if angle between force and displacement is acute or both are in same direction A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

444 | Give few examples where displacement of an object is in the direction opposite to the force acting on the object. | 11 |

445 | The balls, having linear momenta ( overrightarrow{mathbf{p}}_{1}= ) ( mathbf{p} hat{mathbf{i}} ) and ( overrightarrow{mathbf{p}}_{2}=-mathbf{p} hat{mathbf{i}}, ) undergo a collision in free space. There is no extemal force acting on the balls. Let ( overrightarrow{mathbf{p}}_{1} ) and ( overrightarrow{mathbf{p}}_{2} ) be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of ( mathbf{p}, mathbf{a}_{1}, mathbf{a}_{2}, mathbf{b}_{1}, mathbf{b}_{2}, mathbf{c}_{1} ) and ( mathbf{c}_{2} ) This question has multiple correct options ( mathbf{A} cdot overrightarrow{mathbf{p}}_{1}=mathbf{a}_{1} hat{i}+mathbf{b}_{1} hat{mathbf{j}}+mathbf{c}_{1} hat{mathbf{k}} ) [ overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} mathrm{i}+mathrm{b}_{2} ] B ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{c}_{1} hat{mathrm{k}} ) [ overrightarrow{mathrm{p}}_{2}=mathrm{c}_{2} hat{mathrm{k}} ] C ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{a}_{1} mathrm{i}+mathrm{b}_{1} hat{mathrm{j}}+mathrm{c}_{1} hat{mathrm{k}} ) [ overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} hat{mathrm{i}}+mathrm{b}_{2} hat{mathrm{j}}-mathrm{c}_{1} hat{mathrm{k}} ] D ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{a}_{1} hat{mathrm{i}}+mathrm{b}_{1} hat{mathrm{j}} ) [ overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} mathrm{i}+mathrm{b}_{1} hat{mathrm{j}} ] | 11 |

446 | A satellite is moving in a circular orbit around earth with a speed ( V ), If its mass is ( mathrm{m} ), then its total energy will be. A ( cdot frac{3}{4} m v^{2} ) B. ( m v^{2} ) c. ( frac{1}{2} m v^{2} ) D. ( -frac{1}{2} m v^{2} ) | 11 |

447 | If vector ( vec{A}=hat{i}+c hat{j}+5 hat{k} ) and vector ( vec{B}=2 hat{i}+hat{j}-hat{k} ) are perpendicular,then calculate the value of ( c ) | 11 |

448 | 91. Figure 8.265 shows a plot of the potential energy as a function of x for a particle moving along the x-axis. Which of the following statement(s) is/are true? UA a b c d Fig. 8.265 a. a, c, and d are points of equilibrium b. a is a point of stable equilibrium c. b is a stable equilibrium point d. All of the above | 11 |

449 | retel NU I Uuno muy ve Ullerent. Tlustration 8.1 A constant force F =(3ỉ +2j+2) N acts on a particle displacing it from a position 7; =(-î +-2) m in a new position r = (i -j + 3k) m. Find the work done by the force. The displacement vector = – | 11 |

450 | A wagon of mass 10 tons moving at a speed of 12 kmph collides with another wagon of mass 8 tons moving on the same track in the same direction at a speed of ( 10 mathrm{kmph} ). If the speed of the first wagon decreases to 8 kmph. Find the speed of the other after collision A. ( 18 mathrm{kmph} ) B. 25 kmph c. ( 5 mathrm{kmph} ) D. ( 15 mathrm{kmph} ) | 11 |

451 | A particle experiences a positiondependent force given by [ boldsymbol{F}(boldsymbol{x})=-boldsymbol{6} boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}+boldsymbol{3} / boldsymbol{x}^{2} ] where ( x ) is in meters and ( F ) is in Newtons (units have been abbreviated). At ( x=1 m, ) what is the potential energy of the particle relative to the potential energy at the origin? A . ( +5 J ) в. ( +3 J ) ( c .-3 J ) D. ( -5 . J ) E. Cannot be determined | 11 |

452 | 70. A force F = (3xy – 5z) ſ + 4 zł is applied on a particle. The work done by the force when the particle moves from point (0, 0, 0) to point (2, 4, 0) as shown in Fig. 8.250 is (2, 4,0) y= x2 (0,0,0) Fig. 8.250 a. 280 units c. 232 units b. 140 units d. 192 units – units | 11 |

453 | The spring shown in figure is unstretched when a man starts pulling the block. The mass of the block is ( M . ) If the man exerts a constant force ( boldsymbol{F} ) The energy stored in the spring when the block passes through the equilibrium position is ( ^{A} cdot frac{2 F^{2}}{k} ) B. ( frac{F^{2}}{k} ) ( ^{mathbf{c}} cdot frac{F^{2}}{4 k} ) D. ( frac{F^{2}}{2 k} ) | 11 |

454 | A man of mass ( 50 k g ) climbs up a ladder of height ( 10 m ). Calculate the increase in his potential energy. ( left(boldsymbol{g}=mathbf{9 . 8 m} boldsymbol{s}^{-2}right) ) A . ( 490 J ) B . ( 2450 J ) c. ( 4900 J ) D. ( 0 . ) | 11 |

455 | 19. The speed of the bob at the highest point on the circle is a. 146 ms b. V26 ms? c. 52 ms -1 d. 135 ms -1 | 11 |

456 | If the work done by the actor is ( y mathrm{kJ} ), find ( 2 y ) | 11 |

457 | Tllustration 8.2 Three constant forces F = 2-3j+2k, És=i+j-k, and Ēz = 3 + j-2k in newtons displace a particle from (1,-1, 2) to (-1,-1, 3) and then to (2,2,0) (displacement being measured in metres). Find the total work done by the forces. | 11 |

458 | Thread is massless. On applying force ( F ) KE increases by ( 20 mathrm{J} ) in ( 1 mathrm{s} ) A. tension in the string is ( mathrm{Mg} ) B. the tension in the string is ( F ) c. work done by the tension in 1 s is 20 J D. the work done by the force of gravity is 20 Jin | 11 |

459 | Three vectors ( overrightarrow{boldsymbol{A}}=boldsymbol{a} overrightarrow{boldsymbol{i}}+overrightarrow{boldsymbol{j}}+overrightarrow{boldsymbol{k}}, overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{i}}+ ) ( boldsymbol{b} overrightarrow{boldsymbol{j}}+overrightarrow{boldsymbol{k}}, overrightarrow{boldsymbol{C}}=overrightarrow{boldsymbol{i}}+overrightarrow{boldsymbol{j}}+boldsymbol{c} overrightarrow{boldsymbol{k}} ) are mutually perpendicular ( (vec{i}, vec{j}, vec{k} ) are unit vectors along ( X, Y, Z ) axis respectively. The respective values of ( a, b ) and ( c ) are ( mathbf{A} cdot 0,0,0 ) B. ( -frac{1}{2},-frac{1}{2},-frac{1}{2} ) c. 1,-1,1 D. ( frac{1}{2}, frac{1}{2}, frac{1}{2} ) | 11 |

460 | Which of the following forms of energy is released or absorbed in most chemical reactions? A. Light energy B. Electrical energy c. sound energy D. Heat energy | 11 |

461 | If the amount of heat given to a system is ( 35 J ) and the amount of work done on the system is ( 15 J ), then the change in internal energy of the system is A. ( -50 J ) в. ( 20 J ) ( c .30 J ) D. ( 50 J ) | 11 |

462 | A force ( (10 hat{i}-3 hat{j}+6 hat{k}) ) newton acts on a body of mass ( 100 g ) and displaces it from ( (6 hat{i}-5 hat{j}-3 hat{k}) ) metre to ( (10 hat{i}-2 hat{j}+7 hat{k}) m ) The work done is ( mathbf{A} cdot 21 J ) в. ( 361 J ) c. ( 121 J ) D. ( 1000 J ) | 11 |

463 | Illustration 8.30 A pendulum of mass m and length suspended from the ceiling of a trolley which has a const acceleration a in the maximum deflection of the pendula from the vertical. Om Fig. 8.64 | 11 |

464 | A car weighing 1 ton is moving twice as fast as another car weighing 2 ton. The kinetic energy of the one-ton car is A. less than that of the two-ton car is B. some as that of the two-ton car is c. more than that of the two-ton car is D. impossible to compare with that of the two-ton car unless the height of each | 11 |

465 | A completely inelastic is one in which the two colliding particles A. split into small fragments flying in all directions B. remain together after the collision. c. are separated after the collision. D. none of the above | 11 |

466 | u. Directly proportional to t 66. A particle of mass m slides on a frictionless surface ABCD, starting from rest as shown in Fig. 8.248. The part BCD is a circular arc. If it looses contact at point P, the maximum height attained by the particle from point C is АО 2R/ – – – IRIR Fig. 8.248 – [2+xb] – asztal c. 3 d. None of these | 11 |

467 | The gravitational potential energy of a body at a distance ( r ) from the centre of earth is ( U . ) Its weight at a distance ( 2 r ) from the centre of earth is A ( cdot frac{U}{r} ) в. ( frac{U}{2 r} ) c. ( frac{U}{4 r} ) D. ( frac{U}{sqrt{2} r} ) | 11 |

468 | A bullet of mass ( 5 g ) travels with a speed of ( 500 m s^{-1} . ) if it penetrates a fixed target which offers a constant resistive force of ( 1000 mathrm{N} ) to the motion of the bullet, find : (a) the initial kinetic energy of the bullet, (b) the distance through which the bullet has penetrated. ( mathbf{A} cdot s=0.625 m ) B. ( s=0.725 mathrm{m} ) ( mathbf{c} cdot s=0.225 m ) D. ( s=0.65 m ) | 11 |

469 | Two billiard balls of the same size and mass are in contact on a billiard table. third ball of the same size and mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the ball is: A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot 2 ) ( overline{3} ) ( D cdot 3 ) ( bar{A} ) | 11 |

470 | Explain why water stored in a dam has potential energy. | 11 |

471 | A ball is let fall from a height ( h_{0} ). It makes ( n ) collisions with the earth. After ( n ) collisions it rebounds with a velocity ( v_{n} ) ‘ and the ball rises to a height ( h_{n} ) then coefficient of restitution is given by: ( ^{mathbf{A}} cdot_{e}=left[frac{h_{n}}{h_{0}}right]^{1 / 2 n} ) ( ^{mathrm{B}} e=left[frac{h_{0}}{h_{n}}right]^{1 / 2 n} ) c. ( _{e}=frac{1}{n} sqrt{frac{h_{n}}{h_{0}}} ) D. ( _{e}=frac{1}{n} sqrt{frac{h_{0}}{h_{n}}} ) | 11 |

472 | A sphere A moving with a speed u and rotating with an angular velocity ( omega ) makes a head-on elastic collision with an identical stationary sphere B. There is no friction between the surface of ( A ) and B. Disregard gravity. Then which of the following statements is/are true? This question has multiple correct options A. A will stop moving but continue to rotate with an angular velocity ( omega ) B. A will come to rest and stop rotating. c. B will move with a speed u without rotating D. B will move with a speed u and rotate with an angular velocity ( omega ) | 11 |

473 | Two bars of masses ( m_{1} ) and ( m_{2} ) connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between the bars and the surface is equal to ( k ). The minimum constant force that has to be applied in the horizontal direction to the bar of mass ( m_{1} ) in order to shift the other bar is ( F_{min }=k gleft(m_{1}+frac{m_{2}}{x}right) ) Find ( x ) | 11 |

474 | Find the components of a vector ( overrightarrow{boldsymbol{A}}= ) ( 2 hat{i}+3 hat{j} ) along the directions of ( hat{i}+ ) ( hat{j} ) and ( hat{i}-hat{j} ) A ( cdot frac{5}{sqrt{2}}, frac{-1}{sqrt{2}} ) B. ( frac{-5}{sqrt{2}}, frac{-1}{sqrt{2}} ) c. ( frac{5}{sqrt{2}}, frac{1}{sqrt{2}} ) D. ( frac{-5}{sqrt{2}}, frac{1}{sqrt{2}} ) | 11 |

475 | A planet of radius ( boldsymbol{R}=frac{mathbf{1}}{mathbf{1 0}} times ) (radiusof Earth) has the same mass density as Earth. Scientists dig a well of depth ( frac{R}{5} ) on it and lower a wire of the same length and of linear mass density ( 10^{-3} k g m^{-1} ) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth ( = ) ( 6 times 10^{6} m ) and the acceleration due to gravity of Earth is ( 10^{-2} ) ) ( mathbf{A} cdot 96 N ) в. ( 108 N ) c. ( 120 N ) D. ( 150 N ) | 11 |

476 | Illustration 8.66 A pump is required to lift 1000 kg of water per minute from a well 20 m deep and eject it at a rate of 20 ms- a. How much work is done in lifting water? b. How much work is done in giving it KE? C. What HP (horsepower) engine is required for the purpose of lifting water? . . DE 1 | 11 |

477 | If angular speed of the rod just after the impact is ( frac{1}{2} sqrt{frac{x g}{2 l}}, ) find the value of ( x ) | 11 |

478 | A ( 20 mathrm{kg} ) object is being lifted through a height of ( mathrm{m} ) when ( 484 mathrm{J} ) of work is done on it. | 11 |

479 | For what (finite) value of ( x operatorname{does} F(x)= ) ( mathbf{0 ?} ) | 11 |

480 | A steel ball moving with a velocity ( bar{v} ) collides with an identical ball originally at rest. The velocity of the first ball after the collision is : A ( cdotleft(-frac{1}{2}right) bar{v} ) в. ( -bar{v} ) c. ( bar{v} ) D. zero | 11 |

481 | A sphere ( A ) moving with speed ( u ) and rotating with an angular velocity ( omega ) makes a head-on elastic collision with an identical stationary sphere ( boldsymbol{B} ). There is no friction between the surfaces of ( boldsymbol{A} ) and ( B . ) Choose the correct alternative(s). Discard gravity. This question has multiple correct options A. ( A ) will stop moving but continue to rotate with an angular velocity ( omega ) B. ( A ) will come to rest and stop rotating C. ( B ) will move with speed ( u ) without rotating D. ( B ) will move with speed ( u ) and rotate with an angular velocity ( omega ) | 11 |

482 | What is the change in potential energy (in calories) of a ( 10 mathrm{kg} ) mass after ( 10 mathrm{m} ) fall? A. 1000 call ( l ) в. ( 0.1 mathrm{kcal} ) c. 238.9 cal D. 23.89 cal | 11 |

483 | An engine can pump 40,000 liters of water to the vertical height of 35 meters in 5 minutes. Calculate the gravitational potential energy of water at given height. | 11 |

484 | The potential energy (in Sl units) of a particle of mass ( 2 k g ) in a conservative field is ( U=6 x-8 y . ) If the initial velocity of the particle is ( vec{u}=-1.5 hat{i}+ ) ( 2 hat{j} ) then the total distance travelled by the particle in first two seconds is: A. ( 10 mathrm{m} ) B. 12m ( c .15 mathrm{m} ) D. 18m | 11 |

485 | sides 2 a lies on a smooth horizontal plane as shown in the figure. Three point masses of mass m each strike the block at ( A, B ) and ( C ) with speeds ( v ) as shown. After the collision, the particles come to rest. Then the angular velocity acquired by the triangular block is (I is the moment of inertia of the triangular block about ( mathrm{G} ), perpendicular to the plane of the block) ( A ) clockwise B. ( frac{2 m v a}{l} ) clockwise ( frac{2 sqrt{3} m v a}{l} ) clockwise D. None of these | 11 |

486 | 59. A particle A of mass 10/7 kg is moving in the positive direction of x-axis. At initial position x = 0, its veloci is 1 ms, then its velocity at x = 10 m is (use the graph given) Power (W) 10 (m) Fig. 8.245 b. 2 ms-1 a. 4 ms-1 c. 312 ms -1 d. 100 3 ms1 | 11 |

487 | 6. Mark the correct statement(s). a. The work-energy theorem is valid only for particle b. The work-energy theorem is an invariant law physics. c. The work-energy theorem is valid only in inertial frames of reference. d. The work-energy theorem can be applied in non- inertial frames of reference too. | 11 |

488 | A bomb at rest at the summit of a cliff breaks into two equal fragments. One of the fragments attains a horizontal velocity of ( 20 sqrt{3} m / s . ) The horizontal distance between the two fragments, when their displacement vectors is inclined at ( 60^{0} ) relative to each other is ( (g=10), m / s^{wedge} 2 $ $ ) A ( cdot 40 sqrt{3} m ) B. ( 80 sqrt{3} m ) c. ( 120 sqrt{3} mathrm{m} ) . D. ( 480 sqrt{3} mathrm{m} ) | 11 |

489 | A satellite of mass ( mathrm{m} ) is orbiting the earth in a circular orbit of radius r. It starts losing energy due to small air resistance at the rate of ( C J s^{-1} ). The time taken for the satellite to reach the earth is: ( frac{G M m}{x C}left[frac{1}{R}-frac{1}{r}right] . ) Find the value of ( boldsymbol{x} ) | 11 |

490 | figure. The system is released from rest and the block of mass 1 kg is found to have a speed ( 0.3 m / s ) after it has descended through a distance of 1 m. The coefficient of kinetic friction between the block and the table is (All pulleys are massless and smooth and strings are inextensible and light acceleration due to gravity ( =10 m / s^{2} . ) ): A . 0.12 B. 0.5 ( c .0 . ) D. 0.15 | 11 |

491 | Sania, a high-board diver of mass ( 50 mathrm{kg} ) is diving from a height of ( 30 mathrm{m} ) into a pool (see figure given). What is the potential energy of Sania at point ( A ) ? ( left(g=10 m s^{-2}right) ) A . ( 5000 J ) в. 10000 . c. ( 15000 J ) D. 20000 | 11 |

492 | A bucket tied to a string is lowered at a constant acceleration of ( g / 4 ). If the mass of the bucket is ( m ) and is lowered by a distance ( d ), the work done by the string on bucket will be:(assume the string to be massless, acceleration due to gravity ( =g) ) A ( cdot frac{1}{4} m g d ) в. ( -frac{3}{4} m g d ) c. ( -frac{4}{3} m g d ) D. ( frac{4}{3} m g d ) | 11 |

493 | If under the action of fore ( boldsymbol{F}=-(boldsymbol{y} hat{boldsymbol{i}}+ ) ( x hat{i} ) ) a particle moves form (0,0) to ( (a, 0) ) then to ( (a, a) ) then find work done by force | 11 |

494 | Where will he have the highest potentia energy? A. In water B. On land ( c . ) on D. ons | 11 |

495 | If a cricket ball hits you, it will hurt much more than a tennis ball would when moving with the same velocity because: A. a cricket ball is bigger B. a cricket ball has more mass c. a cricket ball has less density D. none of the above | 11 |

496 | 38. A particle of mass m moves with a variable velocity v, which changes with distance covered x along a straight line as v=k vx , where k is a positive constant. The work done by all the forces acting on the particle, during the first t seconds is a. mk4 b. mk4,2 c. mk4 2 d. mk42 16 | 11 |

497 | Two,weights of ( 5 mathrm{kg} ) and ( 10 mathrm{kg} ) are placed on a horizontal table of height ( 1.5 mathrm{m} ) Which weight will have more potential energy? ( A cdot 5 mathrm{kg} ) в. ( 10 mathrm{kg} ) c. Both will have equal energy D. None of the above | 11 |

498 | Assertion In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason In an elastic collision, the linear momentum of the system is conserved. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

499 | When a body of mass ( 1.0 mathrm{kg} ) is suspended from a certain light spring hanging vertically, its length increases by ( 5 mathrm{cm} . ) By suspending ( 2.0 mathrm{kg} ) block to the spring and if the block is pulled through ( 10 mathrm{cm} ) and released, the maximum velocity in it in ( m / s ) is A . 0.5 B. 1 c. 2 D. 4 | 11 |

500 | A mass of ( 3 mathrm{kg} ) is dropped from alower of ( 125 mathrm{m} ) high. After 3 s its ( mathrm{K} ). E. will be : A . 1300 J B. 1050 J c. 750 D. 550 | 11 |

501 | Two identical buggies each of mass ( M ) moves one after due to inertia (without friction) with the some velocity. A man of mass ( m ) rides the rear buggy. At a certain moment, the manjumps into the front buggy with velocity relative to this buggy. Knowing that the mass of each buggy is equal to ( M ). Find the velocity with which the buggies will move after that. | 11 |

502 | A body of mass ( m ) is accelerated to velocity ( v ) in time ( t^{prime} . ) The work done by the force as a function of time ( t ) will be A ( cdot frac{m}{2} frac{v^{2} t^{2}}{t^{2}} ) B ( cdot frac{1}{2}left(frac{m v}{t^{prime}}right)^{2} t^{2} ) c. ( frac{m v}{2 t^{prime}} t^{2} ) D. ( frac{m v t^{2}}{2 t^{prime}} ) | 11 |

503 | A rifle bullet loses ( 1 / 20 ) th of its velocity in passing through a plank. Assuming constant resistive force, the least number of such planks required just to stop the bullet is: A . 15 B. 10 ( c cdot 11 ) D. 20 | 11 |

504 | A body starts from rest with uniform acceleration and acquires a velocity ( boldsymbol{v} ) in time ( T . ) The instantaneous kinetic energy of the body at time ( t ) is proportional to: ( mathbf{A} cdot(v / T) t ) B ( cdotleft(v^{2} / Tright) t^{2} ) C ( cdotleft(v^{2} / T^{2}right) t ) D. ( left(v^{2} / T^{2}right) t^{2} ) | 11 |

505 | Suppose that the acceleration of a free fall at the surface of a distant planet was found to be equal to that at the surface of the earth. If the diameter of the planet were twice the diameter of the earth, then the ratio of mean density of the planet to that of the earth would be: A . 4: 1 B . 2: 1 c. 1: 1 D. 1: 2 | 11 |

506 | A moving body makes a perfectly inelastic collision with a second body of equal mass at rest K.E lost during collision is of initial K.E. A ( cdot 1 / 4 ) B. 1/2 ( c ) D. | 11 |

507 | A single conservative force ( F(x) ) acts on a ( 1.0 k g ) particle that moves along the ( x- ) axis.The potential energy U(x) is given by ( U(x)=20+(x-2)^{2} ) where ( x ) is in meters.At ( x=5.0 m, ) the particle has a kinetic energy of 20 J. What is the mechanical energy of the system? | 11 |

508 | Work done in lifting a body is calculated by A. Mass of the body ( times ) vertical distance moved B. Force acting on a body ( times ) vertical distance moved C. Weight acting on the body ( times ) vertical distance moved D. None of the above | 11 |

509 | A rubber develops a force ( boldsymbol{F}=(-2 x+ ) 1) ( N, ) (Where ( x ) is the extension in its natural length in ( m ) ). Work done by the force when rubber is stretched from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{1} boldsymbol{m} ) is : A . ( 4 J ) B. ( 8 J ) c. ( Z ) ero D. ( 10 J ) | 11 |

510 | The energy released in a modest size atomic bomb (20 kiloton) is about ( 10^{14} ) J. On a monsoon day in Mumbai, there was a heavy rainfall of about 100 ( mathrm{cm} ) over an area of about ( 100 mathrm{km}^{2} ). The energy released in the atmosphere on that day is roughly equivalent to that released in: (Assume average height of clouds to be ( 2000 mathrm{m} ) A. 20 atomic bombs B. 100 atomic bombs c. Atomic bomb D. Negligible compared to an atomic bomb | 11 |

511 | Three vectors ( vec{A}, vec{B}, vec{C} ) satisfy the relation ( vec{A} cdot vec{B}=0 ) and ( vec{A} cdot vec{C}=0 . ) The vector ( vec{A} ) is parallel to A ( cdot vec{B} ) в. ( vec{c} ) c. ( vec{B} cdot vec{C} ) D . ( vec{B} times vec{C} ) | 11 |

512 | A ball is projected upwards. As it rises, there is increase in its: A. Momentum B. Retardation c. Kinetic energy D. Potential energy | 11 |

513 | During inelastic collision between two bodies, which of the following quantities always remain conserved? A. Total kinetic energy B. Total mechanical energy c. Total linear momentum. D. speed of each body | 11 |

514 | Three particles with masses 10,20 and 40 g are moving with velocities ( 10 hat{i}, 10 hat{j} ) and ( 10 hat{k} m / ) sec respectively. If due to some interaction the first particle comes to rest and the velocity of second becomes ( (3 hat{i}+4 hat{j} m / s e c) . ) Then the velocity of third particle after their interaction is: ( mathbf{A} cdot hat{i}+hat{j}+5 hat{k} ) в. ( hat{j}+10 hat{k} ) c. ( hat{i}+hat{j}+10 hat{k} ) D. ( hat{i}+3 hat{j}+10 hat{k} ) | 11 |

515 | A body of mass ( M ) (figure shown above) with a small disc of mass ( m ) placed on it rests on a smooth horizontal plane. The disc is set in motion in the horizontal direction with velocity ( v . ) The height (relative to the initial level) to which the disc rise after breaking off the body ( M ) is given as ( h= ) ( frac{M v^{2}}{x g(M+m)} . ) The friction is assumed to be absent. Find ‘ ( x ) ‘. | 11 |

516 | Given ( vec{A}=2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}+hat{j} . ) The component of vector ( overrightarrow{boldsymbol{A}} ) along vector ( overrightarrow{boldsymbol{B}} ) is: A ( cdot frac{1}{sqrt{2}} ) B. ( frac{3}{sqrt{2}} ) c. ( frac{5}{sqrt{2}} ) D. ( frac{7}{sqrt{2}} ) | 11 |

517 | Find the moment ( t_{0} ) at which the velocity vector forms an angle ( frac{pi}{4} ) with the acceleration vector. A ( t_{0}=frac{1}{3 alpha} ) в. ( t_{0}=frac{2}{alpha} ) c. ( _{t_{0}}=frac{3}{alpha} ) D ( t_{0}=frac{1}{alpha} ) | 11 |

518 | The energy released on burning coal, oil, wood or gas is: A. kinetic energy B. heat energy c. light energy D. solar energy | 11 |

519 | A cord is used to lower vertically a block of mass ( M ) by a distance ( d ) with constant downward acceleration ( boldsymbol{g} / mathbf{4} ) Work done by the cord on the block is: A ( cdot_{M g} frac{d}{4} ) в. ( 3 M g frac{d}{4} ) c. ( _{-3 M g_{overline{4}}^{d}} ) D. ( M g d ) | 11 |

520 | A moving body weighing ( 400 N ) possesses ( 500 J ) of kinetic energy. Calculate the velocity with which the body is moving. ( left(boldsymbol{g}=mathbf{1 0 m s}^{-1}right) ) | 11 |

521 | A man of 30 kg jumps up to a height of ( 2 mathrm{m} . ) What is his potential energy at the highest point? A. 60 J B. 50 J c. 15 J D. 600 J | 11 |

522 | If the mass of the moving object is decreased ( 1 / 4 ) of its mass and its velocity is increased to twice its previous velocity, what will be the kinetic energy of the object from the following? A. ( 1 / 2 ) of the previous kinetic energy B. 4 times of previous kinetic energy c. Kinetic energy will remain constant D. 2 times of the previous kinetic energy | 11 |

523 | A tennis ball is released from height ( h ) above ground level. If the ball makes inelastic collision with the ground, to what height will it rise after third collision, e is the coefficient resitiution between ball and ground? A ( cdot h e^{6} ) B ( cdot e^{2} h ) ( mathbf{c} cdot e^{3} h ) D. None of these | 11 |

524 | The angle between ( overrightarrow{boldsymbol{R}}=mathbf{2} hat{mathbf{i}}+mathbf{3} hat{boldsymbol{j}}-mathbf{4} hat{boldsymbol{k}} ) and y-axis is ( ^{mathrm{A}} cdot cos ^{-1}left(frac{2}{sqrt{29}}right) ) в. ( cos ^{-1}left(frac{3}{sqrt{29}}right) ) ( ^{mathrm{c}} cdot sin ^{-1}left(frac{3}{sqrt{29}}right) ) D ( cdot tan ^{-1}left(frac{3}{sqrt{29}}right) ) | 11 |

525 | A piece of stone placed on the roof possesses A. kinetic energy B. potential energy c. thermal energy D. nuclear energy | 11 |

526 | One of the rectangular components of a force of ( 50 N ) is ( 30 N . ) The other rectangular component will be A . ( 40 N ) в. ( 30 N ) ( c .35 N ) D. ( 45 N ) | 11 |

527 | • 110 TO 15 Cous 48. Speed of the particle at A will be nearly a. 4.0 ms-1 b. 2.8 ms- c. 3.6 ms-d. 5.6 ms-1 | 11 |

528 | та – Un 23. Which of the following options is correct regarding the various work done? a. Wgravity = -mgh b. W friction > 0 c. Wman = mgh+ -mv2 d. Wfriction = 0 | 11 |

529 | A force of ( 10 mathrm{N} ) acts on a body of ( 2 mathrm{kg} ) mass for a distance of ( 1 mathrm{m} ). The kinetic energy received by the body is: A . 20 B. 10 J c. 5 J D. 2.5 | 11 |

530 | A coconut fruit hanging high in a palm tree has ………. owing to its location. A. Free energy B. Kinetic energy c. Activation energy D. Potential energy | 11 |

531 | Two balls ( A ) and ( B ) having masses ( 1 k g ) and ( 2 k g, ) moving with speeds ( 21 m / s ) and ( 4 m / s ) respectively in opposite direction, collide head on. After collision ( A ) moves with a speed of ( 1 m / s ) in the same direction, the correct statements is : This question has multiple correct options A. The velocity of ( B ) after collision is ( 6 m / s ) opposite to the direction of motion before collision B. The coefficient of restitution is 0.2 c. The loss of kinetic energy due to collision is 200 J D. The impulse of the force between the two balls is ( 40 mathrm{Ns} ) | 11 |

532 | A plot of velocity versus time is shown in figure. A single force acts on the body. The correct statement is? A. In moving from ( C ) to ( D ), work done by the force on the body is positive B. In moving from ( B ) to ( C ), work done by the force on the body is positive C. In moving from ( A ) to ( B ), the body does work on the system D. In moving from ( O ) to ( A ), work is done by the body and is negative | 11 |

533 | 25. A body of mass 1 kg is taken from infinity to a point When the body reaches that point, it has a speed of 2 me1 The work done by the conservative force is – 5 J. Which of the following is true (assuming non-conservative and pseudo-forces to be absent). a. Work done by the applied force is +7 J. b. The total energy possessed by the body at Pis +7J. c. The potential energy possessed by the body at Pis +5 d. Work done by all forces together is equal to the change in kinetic energy. | 11 |

534 | What is kinetic energy? Derive an equation for the kinetic energy of a body of mass ‘ ( m ) ‘ moving at a speed ‘ ( v ) ‘ | 11 |

535 | The vector ( vec{c} ) is perpendicular to the vectors ( overrightarrow{boldsymbol{a}}=(mathbf{2},-mathbf{3}, mathbf{1}), overrightarrow{boldsymbol{b}}=(mathbf{1},-mathbf{2}, mathbf{3}) ) and satisfies the condition ( vec{c} .(hat{i}+2 hat{j}- ) ( mathbf{7} hat{k})=10 . ) Then the vector ( hat{c}= ) ( A cdot(7,5,1) ) B. (-7,-5,-1) ( c cdot(1,1,-1) ) ( c ) ( D . ) none | 11 |

536 | Illustration 8.63 A car of mass 500 kg moving with a speed 36 kmh in a straight road unidirectionally doubles its speed in 1 min. Find the power delivered by the engine. | 11 |

537 | The amount of work done in lifting a mass ‘ ( m ) ‘ from the surface of the earth to height ( 2 R ) is A. ( 2 m g R ) в. ( 3 m g R ) c. ( frac{3}{2} m g R ) D. ( frac{2}{3} m g R ) | 11 |

538 | The mass of the particle is 2 kg. It is projected as shown in four different ways with same speed of ( 10 mathrm{m} / mathrm{s} / ). Find out the work done by gravity by the time the stone fails on ground. A. 2000 B. 4000 J c. 6000 J D. 8000 J | 11 |

539 | If ( g ) is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( mathrm{m} ) raised from the surface of the earth to a height equal to the radius ( mathrm{R} ) of the earth, is: ( mathbf{A} cdot 2 mathrm{mgR} ) в. ( frac{1}{2} mathrm{mgR} ) c. ( frac{1}{4} mathrm{mgR} ) D. mgn | 11 |

540 | Assertion (A) : The value of coefficient of restitution is independent of the masses and velocities of the colliding bodies but depends on their materials. Reason (R) : Coefficient of restitution is the ratio of the relative velocity of separation or the relative velocity of approach A. Both Assertion (A) and Reason (R) are correct and R is the correct explanation B. Both Assertion (A) and Reason (R) are correct but the reason does not give the correct explanation c. A is true but R is false D. A is false but R is true | 11 |

541 | A ball ( A ) is moving with velocity ( 5 m / s ) collides elastically with another identical ball ( B ) which is initially at rest such that the velocity of ( B ) after the collision makes an angle of ( 37^{circ} ) with the initial velocity of ( A ). Then the INCORRECT statement is : A. speed of ( A ) after collision is ( 3 m / s ) B. Speed of ( B ) after collision is ( 4 m / s ) c. Balls ( A ) and ( B ) move at right angle after collision D. Kinetic energy is not conserved as the collision is not head on | 11 |

542 | A metallic wire of length ( L ) metre extends by ( ell ) metre when stretched by suspending a weight ( M g ) from it. The mechanical energy stored in the wire is ( mathbf{A} cdot 2 M g ell ) в. ( M g ell ) c. ( frac{M g ell}{2} ) D. ( frac{M g ell}{4} ) | 11 |

543 | From a water fall, water is pouring down at the rate 100 kg per see on the blade of a turbine. If the height of the fall be 100 ( mathrm{m}, ) the power delivered to the turbine is approximately equal to A. ( 100 mathrm{kW} ) B. 1 ( w ) ( c cdot 1 k w ) D. 100 ( w ) | 11 |

544 | No work is said to have been done when an object moves at an angle of with the direction of the force. A. 0 B. 90 ( c cdot 180 ) D. Between 90 and 180 | 11 |

545 | ( operatorname{Let} vec{A}=(hat{i}+hat{j}) ) and, ( vec{B}=(2 hat{i}-hat{j}) . ) The magnitude of a coplanar vector ( overrightarrow{boldsymbol{C}} ) such that ( vec{A} cdot vec{C}=vec{B} cdot vec{C}=vec{A} cdot vec{B}, ) is given by: A ( cdot sqrt{frac{10}{9}} ) B. ( sqrt{frac{5}{9}} ) c. ( sqrt{frac{-09}{2}^{9}} ) D. ( sqrt{frac{9}{12}} ) | 11 |

546 | A particle moves under the effect of a force ( F=c x ) from ( x=0 ) to ( x=x_{1}, ) the work done in the process is A ( cdot c x_{1}^{2} ) B. ( frac{1}{2} c x_{1}^{2} ) ( c cdot 2 c x_{1}^{2} ) D. zero | 11 |

547 | A ball of mass ( 5 k g ) experience a force ( F=2 x^{2}+x . ) Work done in displacing the ball by ( 2 mathrm{m} ) is then A ( cdot frac{22}{3} J ) в. ( frac{44}{3} J ) c. ( frac{32}{3} J ) D. ( frac{16}{3} J ) | 11 |

548 | A block of mass 2 kg. is free to move along the ( x ) -axis. It is at rest and from ( t=0 ) onwards it is subjected to a time- dependent force ( F(t) ) in the ( x ) direction. The force ( F(t) ) varies with ( t ) as shown in the figure. The kinetic energy of the block after 4.5 second is : | 11 |

549 | Identify the correct statement of Work- Energy Theorem: A. Work done by all the forces on a particle to displace it is equal to its change in kinetic energy. B. Work done by all the forces on a particle is equal to its change in mechanical energy C. Work done by all the forces acting on a particle is equal to change in its potential energy. D. Work done by a force on a particle is equal to change in its kinetic energy. | 11 |

550 | If ( vec{A} ) is perpendicular to ( vec{B}, ) then ( mathbf{A} cdot vec{A} times vec{B}=0 ) B . ( vec{A} cdot[vec{A}+vec{B}]=A^{2} ) c. ( vec{A} cdot vec{B}=A B ) D. ( vec{A} cdot[vec{A}+vec{B}]=A^{2}+A B ) | 11 |

551 | The velocity of a car increases from ( 54 k m / h ) to ( 72 k m / h . ) If the mass of the car is ( 1500 k g, ) find the work done to increase the velocity. A . ( 27000 J ) в. ( 131250 J ) c. ( 0 . ) D. ( 1500 J ) | 11 |

552 | A body is dropped from height 8 m. After striking the surface it rises to ( 6 m ) what is the fractional loss in kinetic energy during impact? Assuming the frictional resistance to be negligible. A . ( 1 / 2 ) в. ( 1 / 4 ) c. ( 1 / 6 ) D. ( 1 / 8 ) | 11 |

553 | An engine draws water from a depth of ( 10 m ) with constant speed ( 2 m / s ) at the rate of ( 10 mathrm{Kg} ) per 10 second The power of the engine is (in ( w a t t): ) (Take: ( g= ) ( 9.8 m / s^{2} ) A. 102 B. 98 ( c .100 ) D. 200 | 11 |

554 | A block of mass m is released from rest onto a spring A ving stiffness ka = mg/2h as shown in Fig. 8.219. If the block compresses spring B through a distance h, find the: m m В llllledagoon Fig. 8.219 a. stiffness of the string B b. equilibrium position of the block c. maximum velocity of the block d. maximum acceleration of the block | 11 |

555 | ( boldsymbol{x}>2 boldsymbol{R} ) ( mathbf{A} cdot frac{2 G M m^{prime}}{(x-r)^{2}}+frac{G m m^{prime}}{(x+r)^{2}} ) ( mathbf{B} cdot frac{G M m^{prime}}{2(x-R)^{2}}+frac{2 G m m^{prime}}{(x-r)^{2}} ) ( mathbf{C} cdot frac{G M m^{prime}}{(x+R)^{2}}+frac{G m m^{prime}}{(x+r)^{2}} ) D. ( frac{G M m^{prime}}{(x-R)^{2}}+frac{G m m^{prime}}{(x-r)^{2}} ) | 11 |

556 | A small ball is suspended from a fixed point ( boldsymbol{O} ) by means of a light and inextensible string of length ( l ). The bal is first taken aside such that string becomes horizontal and then released from rest. At the bottom it collides with a fixed obstacle. The coefficient of restitution is ( e . ) Find the maximum angular deflection of the string after ( n ) th collision | 11 |

557 | 16. Power supplied to a particle of mass 2 kg varies with time as P = 37/2 W. Here t is in second. If the velocity of particle at t=0 is v= 0, the velocity of particle at time t = 2 s will be a. 1 ms-1 b. 4 ms-1 c. 2 ms- d. 272 ms- | 11 |

558 | What is the magnitude of angular velocity of the stick plus puck after the collision? A ( cdot frac{6 v_{i}}{5 l} ) в. ( frac{5 v_{i}}{6 l} ) c. ( frac{v_{i}}{l} ) D. ( frac{v_{i}}{sqrt{2} i} ) | 11 |

559 | A steel ball is dropped from a height ( h_{0} ) The collision of the ball with the floor is inelastic with coefficient of restitution e. Then, the height up to which the ball will rise after second collision is : ( mathbf{A} cdot e^{4} h_{0} ) B. 2eh ( c cdot e^{2} h_{0} ) D. ( e^{-2} h_{0} ) | 11 |

560 | q.1 A block is released from rest from a height ( h=5 ) m. After traveling through the smooth curved surface it moves on the rough horizontal surface through length ( I=8 mathrm{m} ) and climb onto the other smooth curved surface through a height h. If ( mu=0.5, ) find ( h ) ( A cdot 2 m ) в. 3 ( c cdot 1 m ) D. zero | 11 |

561 | A bob of mass ( m ), suspended by a string of length ( l_{1} ) is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass ( m ) suspended by a string of length ( l_{1}, ) which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio ( l_{1} / l_{2} ) is ( mathbf{A} cdot mathbf{1} ) B. 3 ( c .5 ) D. ( 1 / 5 ) | 11 |

562 | The radius of earth is about ( 6400 mathrm{km} ) and that ofmars is ( 3200 mathrm{km} ). The mass of the earth is 10 times the mass of mars. An object weight ( 200 mathrm{N} ) on the surface of earth. Its weight on the surface of mars will be. A. 80 N B. 40 N ( c . ) 20 ( D cdot 8 N ) | 11 |

563 | A small block of superdene material has mass ( 2 times 10^{24} ) kg. It isn’t at a height ( h<<R ). It falls towards earth. Find its speed when it is at a height ( h / 2 ) A ( cdot sqrt{frac{2 g h}{3}} ) в. ( sqrt{frac{3 g h}{4}} ) c. ( sqrt{frac{2 g h}{5}} ) D. ( sqrt{frac{g h}{2}} ) | 11 |

564 | A block of mass ( m ) moving with speed ( v ) collides with another block of mass ( 2 m ) at rest. The lighter block comes to rest after collision. What is the value of coefficient of restitution? A ( cdot frac{1}{2} ) B. ( frac{1}{3} ) ( c cdot frac{3}{4} ) D. ( frac{1}{4} ) | 11 |

565 | A ball is thrown vertically downwards from a height of ( 20 mathrm{m} ) with an initial velocity ( v_{0} . ) It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity ( v_{0} ) is (Take ( boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2} mathbf{)} ) A ( cdot 10 m s^{-1} ) B. ( 14 mathrm{ms}^{-1} ) ( mathrm{c} cdot 20 mathrm{ms}^{-1} ) D. ( 28 m s^{-1} ) | 11 |

566 | A box of mass ( 50 k g ) is pulled along on an inclined plane of ( 12 m ) length and ( 2 m ) height by a constant force of ( 100 N ) from rest. It acquires a velocity of ( 2 m / s ) when it reaches the top of the plane. The work done against friction in joules is A . 50 B. 100 ( c cdot 150 ) D. 200 | 11 |

567 | A heavy steel ball of mass greater than ( 1 mathrm{kg} ) moving with a speed of ( 2 mathrm{m} / mathrm{s} ) collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision the ping pong ball moves approximately with a speed A. ( 2 m / s ) в. ( 4 m / s ) c. ( 2 times 10^{4} m / s ) D. ( 2 times 10^{3} mathrm{m} / mathrm{s} ) | 11 |

568 | A bullet of mass ( m ) is fired with a velocity ( v ) into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is A ( cdot frac{m v}{2 s^{2}} ) в. ( frac{m v^{2}}{2 s} ) c. ( frac{2 s}{m v^{2}} ) D. ( frac{m s^{2}}{2 v} ) | 11 |

569 | A bullet of mass ( A ) and velocity ( B ) is fired into a block of wood of mass ( C . ) If loss of any mass and friction be neglected, then velocity of the system must be ( ^{text {A }} cdot frac{A B}{A+C} ) в. ( frac{A+C}{B+C} ) c. ( frac{A C}{B+C} ) D. ( frac{A+B}{A C} ) | 11 |

570 | In the figure ( m_{1} ) and ( m_{2}left(m_{1}<m_{2}right) ) are joined together by a pulley. When the mass ( m_{1} ) is released from the height ( h ) above the floor, it strikes the floor with speed (Given: Acceleration due to gravity ( =g ) ) A ( cdot sqrt{2 g hleft(frac{m_{1}-m_{2}}{m_{1}+m_{2}}right)} ) в. ( sqrt{2 g h} ) c. ( sqrt{frac{2 m_{2} g h}{m_{1}+m_{2}}} ) D. ( sqrt{frac{2 m_{1} g h}{m_{1}+m_{2}}} ) | 11 |

571 | A mass of ( 10 mathrm{kg} ) is at a point ( mathrm{A} ) on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer | 11 |

572 | Two particles of masses ( m_{1}, m_{2} ) movie with initial velocities ( u_{1} ) and ( u_{2} . ) On collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be ( v_{1} ) and ( v_{2} ) then we must have : A ( cdot frac{1}{2} m_{1} u_{1}^{2}+frac{1}{2} m_{2} u_{2}^{2}=frac{1}{2} m_{1} v_{1}^{2}+frac{1}{2} m_{2} v_{2}^{2}-varepsilon ) B. ( frac{1}{2} m_{1} u_{1}^{2}+frac{1}{2} m_{2} u_{2}^{2}+varepsilon=frac{1}{2} m_{1} v_{1}^{2}+frac{1}{2} m_{2} v_{2}^{2} ) c. ( frac{1}{2} m_{1}^{2} u_{1}^{2}+frac{1}{2} m_{2}^{2} u_{2}^{2}-varepsilon=frac{1}{2} m_{1}^{2} v_{1}^{2}+frac{1}{2} m_{2}^{2} v_{2}^{2} ) D. ( m_{1}^{2} u_{1}+m_{2}^{2} u_{2}-varepsilon=m_{1}^{2} v_{1}+m_{2}^{2} v_{2} ) | 11 |

573 | A ball is dropped from a height ( h ) on a floor of coefficient of restitution ( e ). The total distance covered by the ball just before the second hit is ( mathbf{A} cdot hleft(1-2 e^{2}right) ) B. ( hleft(1+2 e^{2}right) ) c. ( hleft(1-e^{2}right) ) ( D cdot h e^{2} ) | 11 |

574 | A sphere of mass ( m_{1} ) in motion hits directly another sphere of mass ( m_{2} ) at rest and sticks to it, the total kinetic energy after collision is ( 2 / 3 ) of their total K.E before the collision. Find the ratio ( boldsymbol{m}_{1}: boldsymbol{m}_{2} ) | 11 |

575 | Which of the following statements is/are correct about work? This question has multiple correct options ( mathbf{A} cdot operatorname{In} ) a certain reference frame, ( W_{text {pseudo force}}+ ) ( W_{text {conservattive force}}+W_{text {non-conservattive force}}+ ) ( W_{text {other forces}}=Delta K ) B. Work done by friction is always negative. C. Work done by a force is defined as the dot product of the force and the displacement of the point of application of force. D. Work done by conservative force in moving a body from ( A ) to ( B= ) potential energy of the body at ( A ) potential energy of the body at B | 11 |

576 | A block ( A ), whose weight is ( 200 N ), is pulled up a slope of length ( 5 m ) by means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) ) as illuminated in figure. By how much has the potential energy of the block ( boldsymbol{A} ) increased? ( A cdot 0 J ) В. ( 750 J ) ( c .600 J ) D. ( 450 J ) | 11 |

577 | Suppose a vertical tunnel is dug along the diameter of the earth, assumed to be a sphere of uniform mass density ( rho ) If a body of mass ( m ) is thrown in this tunnel, its acceleration at a distance ( y ) from the centre is given by: A. [ frac{4 pi}{3} G rho y m ] B. [ frac{3}{4} pi rho y ] ( c ) [ frac{4}{3} pi rho y ] ( D ) [ frac{4}{3} pi G rho y ] | 11 |

578 | A man of mass ( mathrm{m} ) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h. ( W_{text {gravity}}= ) work done by gravity on the man ( W_{text {friction}}= ) work done by gravity on the man ( W_{text {man }}= ) work done by man Which of the following options is correct regarding the various work done? This question has multiple correct options ( mathbf{A} cdot W_{g r a v i t y}=-m g h ) B. ( W_{f r i t t i o n}>0 ) ( mathbf{c} cdot W_{m a n}=m g h+frac{1}{2} m v^{2} ) D. ( W_{f r i t i o n}=0 ) | 11 |

579 | Why does the grinding wheels have length mass and moderate diameter? | 11 |

580 | 10. The potential energy of the balloon a. Decreases by mgh b. Increases by mgh c. Increases by mg(l – h) d. Increases by mgl | 11 |

581 | Two vectors ( vec{A} ) and ( vec{B} ) have magnitudes ( A=3.00 ) and ( B=3.00 . ) Their vector product is ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}=-mathbf{5 . 0 0 hat { k }}+mathbf{2 . 0 0 hat { mathbf { i } }} ) What is the angle between ( vec{A} ) and ( vec{B} ) ? ( ^{mathrm{A}} cdot sin ^{-1}left[frac{sqrt{29}}{9}right] ) ( ^{mathrm{B}} cdot_{cos ^{-1}}left[frac{sqrt{29}}{9}right] ) ( ^{mathrm{c}} cdot sin ^{-1}left[frac{sqrt{29}}{10}right] ) D. ( sin ^{-1}left[frac{sqrt{29}}{19}right] ) | 11 |

582 | 37. During the first half of the motion, applied force transfers more energy to the a. Kinetic energy b. Potential energy c. Equal to both d. Depends upon mass of the block | 11 |

583 | A ball collides with a smooth fixed wall with a velocity ( 10 mathrm{m} / mathrm{s} ) and returns with a velocity 6 m/s. Considering oblique collision, the coefficient of restitution ( e ) can not be: A . 0.8 B. 0.6 c. 0.5 D. 0.4 | 11 |

584 | A man has a strange ability to jump from any height to another with ease The manjumps to P then to Q, R, S, T and then into water. For which jump will he require the. highest energy? A. Land to B. s to ( c cdot Q ) to ( R ) D. R to | 11 |

585 | A boy carrying a box on his head is walking on a level road from one place to another on a straight road is doing no work against gravity. A. True B. False | 11 |

586 | A smooth rubber cord of length ( l ) whose coefficient of elasticity is ( k ) is suspended by one end from the point ( boldsymbol{O} ) (figure shown above). The other end is fitted with a catch ( B . ) A small sleeve ( A ) of mass ( m ) starts falling from the point O. Neglecting the masses of the thread and the catch, find the maximum elongation of the cord. | 11 |

587 | A ball is dropped from a height h. If the coefficient of restitution be e, then to what height will it rise after jumping twice from the ground? ( A cdot e h / 2 ) B. 2 en ( c cdot e h ) D. ( e^{4} h ) | 11 |

588 | A sphere of mass ( m ) moving with a constant velocity ( boldsymbol{v} ) hits another stationary sphere of the same mass. If ( e ) is the coefficient of restitution, then the ratio of the velocities of the first sphere to the second spheres after the collision will be : A ( cdotleft(frac{1+e}{1-e}right) ) B ( cdotleft(frac{e-1}{e+1}right) ) c. ( left(frac{1-e}{e+1}right) ) D. ( left(frac{1+e}{e-1}right) ) | 11 |

589 | A body of mass 5 kg at rest is under the action of a force which gives it a velocity given by ( v=3 t mathrm{m} / mathrm{s}, ) here ( t ) is time in seconds. The work done by the force in two seconds will be: ( mathbf{A} cdot 90 J ) B. ( 45 J ) ( c .180 J ) D. ( 30 J ) | 11 |

590 | ( K ) is the force constant of a spring. The work done in increasing its extension from ( l_{1} ) to ( l_{2} ) will be: ( mathbf{A} cdot Kleft(l_{2}-l_{1}right) ) в. ( frac{K}{2}left(l_{2}+l_{1}right) ) ( mathbf{c} cdot Kleft(l_{2}^{2}-l_{1}^{2}right) ) D. ( frac{K}{2}left(l_{2}^{2}-l_{1}^{2}right) ) | 11 |

591 | A particle is projected at ( 60^{circ} ) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is? ( A cdot K ) B. zero c. ( K / 4 ) D. ( K / 2 ) | 11 |

592 | Two particles of masses ( m_{1} ) and ( m_{2} ) in projectile motion have velocities ( v_{1} ) and ( v_{2} ) respectively at time ( t=0 . ) They collide at time ( t_{0} . ) Their velocities become ( v_{1}^{prime} ) and ( v^{prime}_{2} ) at time ( 2 t_{0} ) while still moving in air. The value of ( left[left(boldsymbol{m}_{1} boldsymbol{v}_{1}^{prime}+boldsymbol{m}_{2} boldsymbol{v}_{2}^{prime}right)-left(boldsymbol{m}_{1} boldsymbol{v}_{1}+boldsymbol{m}_{2} boldsymbol{v}_{2}right)right] ) A . zero в. ( left(m_{1}+m_{2}right) g t_{0} ) c. ( 2left(m_{1}+m_{2}right) g t_{0} ) D. ( frac{1}{2}left(m_{1}+m_{2}right) g t_{0} ) | 11 |

593 | Block A is hanging from a vertical spring and is at rest. Block B strikes the block A with velocity v and sticks to it. Then the value of ( v ) for which the spring just attains natural length is : ( A ) [ sqrt{frac{60 m g^{2}}{k}} ] в. [ sqrt{frac{6 m g^{2}}{k}} ] c. ( sqrt{frac{10 m g^{2}}{k}} ) D. none of these | 11 |

594 | Find the angular velocity of the rod after the collision. A ( cdot omega=frac{3 v}{(4+eta) l} ) B. ( omega=frac{12 v}{(4+eta) l} ) c. ( omega=frac{3 v}{(4-eta) l} ) D. ( _{omega}=frac{12 v}{(4-eta) l} ) | 11 |

595 | A cubical vessel of height ( 2 mathrm{m} ) is full of water. The work done in pumping the water out of the vessel is? A . ( 72.3 mathrm{kJ} ) B. ( 78.4 mathrm{kJ} ) c. ( 64.5 mathrm{kJ} ) D. ( 57.9 mathrm{kJ} ) | 11 |

596 | ( x ) a small block is projected along it’s length with velocity ( v ) towards front. Coefficient of restitution for each collision is ( e . ) The cart rests on a smooth ground and can move freely. The time taken by block to come to rest w.r.t. cart is : A ( cdot frac{e d}{(1-e) v} ) B. ( frac{e d}{(1+e) v} ) ( c cdot d ) ( bar{e} ) D. infinite | 11 |

597 | Kinetic energy of a body depends on its: A. Position B. Velocity c. shape D. colour | 11 |

598 | A uniform flexible chain of mass ( mathrm{m} ) and length ( 2 ell ) hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain slips over the pin. The speed of chain when it leaves pin is в. ( sqrt{g ell} ) c. ( sqrt{4 g ell} ) D. ( sqrt{3 g ell} ) | 11 |

599 | The change in the value of ( g ) at a height ( h ) above the surface of earth is the same as at a depth ( d ) below the earth. When both ( d ) and ( h ) are much smaller than the radius of earth, then which one of the following is correct? ( ^{A} cdot_{d}=frac{h}{2} ) B. ( d=frac{3 h}{2} ) c. ( d=2 h ) ( mathbf{D} cdot d=h ) | 11 |

600 | The weight of a person on a planet ( A ) is about half that on the Earth. He can jump upto ( 0.4 mathrm{m} ) height on the surface of the Earth. How high he can jump on the planet ( A ) ? ( mathbf{A} cdot 0.4 mathrm{m} ) B. ( 0.2 mathrm{m} ) c. ( 0.8 mathrm{m} ) D. ( 1.6 mathrm{m} ) | 11 |

601 | A uniform chain has a mass ( m ) and length ( l ). It is held on a frictionless table with two third of its length hanging over the edge. Find the work done injust pulling the hanging part back on the table. | 11 |

602 | A heavier body moving with certain velocity collides head on elastically with a lighter body at rest. Then A. smaller body continues to be in the same state of rest B. smaller body starts to move in the same direction with same velocity as that of bigger body c. the smaller body starts to move with twice the velocity of the bigger body in the same direction D. the bigger body comes to rest | 11 |

603 | A ball is dropped from a height of ( 10 mathrm{m} ) If the energy of the ball reduces by ( 40 % ) after striking the ground, how high can the ball bounce back? ( left(g=10 m s^{-2}right) ) ( A cdot 6 m ) B. 10 ( m ) ( c cdot 3 m ) D. 12 | 11 |

604 | 5. A block of mass m is released from rest at point A. The compression in spring (force constant k) when the speed of block is maximum is found to he nmg cos e 2. What should be the value of n? 4k u=0 Fig. 8.300 | 11 |

605 | (a) ( A ) ball of mass ( m ) is thrown vertically upward from the ground with an initial speed ( v, ) its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed again before striking the ground. It implies that the magnitude of initial and final momentum of the ball are same. Yet, it is not an example of conservation of momentum. Explain why? (b) A bullet of mass 20 g is horizontally fired with a velocity ( 150 m s^{1} ) from a pistol of mass 2 kg. What is the recoil velocity of the pistol? | 11 |

606 | Two particles of equal mass m have respective initial velocties ( u hat{i} ) and ( uleft(frac{hat{i}+hat{j}}{2}right) . ) They collide completely inelastically. The energy lost in the process is? A ( cdot frac{1}{3} m u^{2} ) B. ( sqrt{frac{2}{3}} m u^{2} ) c. ( frac{3}{4} m u^{2} ) D. ( frac{1}{8} m u^{2} ) | 11 |

607 | 3. n balls each of mass m impinge elastically each second on a surface with velocity u. The average force experienced by the surface will be a. mnub . 2 mnu c. 4 mnu d. mnu/2 | 11 |

608 | State the energy conversion taking place in a solar cell. | 11 |

609 | Underline the correct alternative: (a) When a conservative force does positive work on a body, the potential energy of the body increases decreases / remains unaltered. (b) Work done by a body against friction always results in a loss of its kinetic / potential energy. (c) The rate of change of total momentum of a many-particle system is proportional to the external force / sum of the internal forces on the system. (d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy / total linear momentum / total energy of the system of two bodies. | 11 |

610 | When an apple falls from a tree what happens to its gravitational potential energyjust as it reaches the ground? | 11 |

611 | Describe the energy transformation taking place in an oscillating pendulum. | 11 |

612 | 71. The potential energy of a particle is determined by the expression U = a (x + y), where a is a positive constant. The particle begins to move from a point with coordinates (3, 3), only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates (1,1) is a. 8 a b. 24a c. 160. d. Zero T 1 | 11 |

613 | A book of mass ( 5 mathrm{kg} ) is placed on a table and it is pressed by ( 10 mathrm{N} ) force then normal force exerted by the table on the book is A . 10 N в. 70 N ( c . ) 59 ( mathrm{N} ) D. 50 N | 11 |

614 | Two bodies of masses ‘ ( m ) ‘ and ‘2m’ are thrown upwards with a velocity of ‘ ( u^{prime} ) and ‘3 ( u ) ‘ from the surface respectively. What is the ratio of their potential energies at the highest point? A . 1: 9 в. 3: 1 ( mathbf{c} cdot 1: 18 ) D. 4: 1 | 11 |

615 | Define the following terms: Kinetic energy. | 11 |

616 | An object is displaced from position vector ( r_{1}=(2 i+3 j) m ) to ( r_{2}=(4 i+6 j) m ) under the action of a force ( F=left(3 x^{2} i+2 y jright) N . ) Finf the work done by this force. | 11 |

617 | A car is moving along a straight level road with constant speed. Then A. The work done on the car is infinite B. The work done on the car is zero c. The work done on the car is a measure of the gravitational potential energy D. The work done on the car cannot be found | 11 |

618 | Force acting on a particles moving in a straight line varies with the velocity ( v ) of the particles as ( boldsymbol{F}=boldsymbol{K} ) where ( boldsymbol{K} ) is a constant. The work done by this force in time ( t ) is A ( cdot frac{K}{v^{2}} t ) в. ( 2 K t ) c. all the above D. None of these | 11 |

619 | Two object collides elastically mass ( 2 m ) is moving with velocity ( U ) and mass ( m ) is initially at rest. After the collision, the objects move away with velocities ( u ) and ( v, ) as shown in above figure. Find the relation between ( u ) and ( v ? ) A ( cdot 2 u cos 30^{circ}=v cos 60^{circ} ) B ( cdot u cos 30^{circ}=2 v cos 60^{circ} ) c. ( 2 u sin 30^{circ}=v sin 60^{circ} ) D. ( u sin 30^{circ}=2 v sin 60^{circ} ) E ( cdot u sin 30^{circ}=v cos 60^{circ} ) | 11 |

620 | Fig. shows a bead of mass ( m ) moving with uniform speed ( v ) through a ( U- ) shaped smooth wire the wire has a semicircular bending between ( A ) and B. Calculate the average force exerted by the bead on the part ( A B ) of the wire. | 11 |

621 | A projectile is fired with the a speed ( u ) at an angle ( theta ) above the horizontal field. The coefficient of restitution be tween the projectile and filed is e. Find the position from the starting point when the projectile will land at its second collision A ( cdot frac{e^{2} u^{2} sin 2 theta}{g} ) B. ( frac{left(1+e^{2}right) u^{2} sin 2 theta}{g} ) ( ^{mathbf{C}} cdot frac{left(1+e^{2}right) u^{2} sin theta cos theta}{g} ) D. ( frac{(1+e) u^{2} sin 2 theta}{g} ) | 11 |

622 | In the game of cricket, the stumps falls when the ball strikes them. This is an example of A. contact force B. Non contact force c. Displacement force D. None | 11 |

623 | A ( 10 k g ) ball is dropped from a height of 10 ( m ). Find (a) the initial potential energy of the ball, (b) the kinetic energy just before it reaches the ground, and (c) the speed just before it reaches the ground. | 11 |

624 | 2. A body is moved along a straight line by a machine deliv- ering constant power. The distance moved by the body in time t is proportional to (IIT JEE, 1984) 2 1/2 b. 3/4 c. 812 d. p. | 11 |

625 | Rakesh lifts a heavy book from the floor of the room and puts it in the book shelf of height ( 2 m . ) In this process, he takes 5 seconds. On which of the following does the work done by him depend? A. Mass of the book and the time taken to do work B. Weight of the book and the height of the book shelf c. Height of the book shelf and the time taken to do work D. Mass of the book, height of the book shelf and the time taken to do work | 11 |

626 | A hollow smooth uniform sphere ( boldsymbol{A} ) of mass ( m ) rolls without sliding on a smooth horizontal surface. It collides elastically and head-on with another stationary smooth hollow sphere ( boldsymbol{B} ) of the same mass mm and same radius. The ratio of the kinetic energy of ( boldsymbol{B} ) to that of ( A ) just after the collision is A . 1: 1 B. 2: 3 ( c cdot 3: 2 ) D. None | 11 |

627 | A body explodes in mid-air. Does its momentum remain conserved? | 11 |

628 | 17. A vehicle of mass m starts moving along a horizontal circle of radius R such that its speed varies with distances covered by the vehicle as c= KVs, where K is a constant. Calculate: a. Tangential and normal force on vehicle as function of b. Distance s in terms of time t. c. Work done by the resultant force in first t seconds after the beginning of motion. | 11 |

629 | A diver stands at the top of a platform that is 15 meters high.After diving, she challenges herself from a cliff that is 30 meters high.since she is twice as far from the surface of the earth when she is on the cliff as compared with the diving board, how does her weight on the cliff compare with her weight on the diving board? A. Her weight on the cliff is half as much B. Her weight on the cliff is one-fourth as much C. Her weight on the cliff is about the same D. Her weight on the cliff is twice as much E. Her weight on the cliff is four times as much | 11 |

630 | The work done in turning a magnet of magnetic moment ( M ) by an angle of ( 90^{circ} ) from the meridian is ( n ) times the corresponding work done to turn it through an angle of ( 60^{circ} . ) Where ( n ) is given by A ( cdot 1 / 2 ) B. 2 c. ( 1 / 4 ) D. | 11 |

631 | Write an expression for the magnitude of the resultant vector ‘R’ of two vectors ( vec{A} ) and ( vec{B} ) acting at a point. When will this resultant vector ‘R’ be maximum? | 11 |

632 | A ball is allowed to fall from a height of ( 10 mathrm{m} . ) If there is ( 40 % ) loss of energy due to impact, then after one impact ball will go upto: A. ( 10 m ) B. ( 8 m ) ( c .4 m ) D. ( 6 m ) | 11 |

633 | 8. A man slowly pulls a bucket of water from a well of depth h = 20 m. The mass of the uniform rope and bucket full of water are m= 200 g and M 19.9 kg, respectively. Find the work done (in kJ) by the man. | 11 |

634 | Water stored in a dam possesses: A. no energy B. electrical energy c. kinetic energy D. potential energy | 11 |

635 | Calculate energy needed for moving a mass of ( 4 k g ) from the centre of the earth to its surface (in joule). If radius of the earth is ( 6400 mathrm{km} ) and acceleration due to gravity at the surface of the earth is ( boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s e c ^ { 2 }} ) A ( cdot 1.28 times 10^{8} J ) в. ( 1.28 times 10^{6} J ) c. ( 2.56 times 10^{8} J ) D. ( 2.56 times 10^{1} 0 J ) | 11 |

636 | If ( |vec{A}+vec{B}|=|vec{A}|=|vec{B}| ) the angle between ( A ) and ( B ) will be :- A ( cdot 90^{circ} ) B . ( 120^{circ} ) ( c cdot 0^{c} ) D. ( 60^{circ} ) | 11 |

637 | A force ( F=-6 x^{3} ) is acting on a block moving along x-axis. Work done by this force is: This question has multiple correct options A. Positive in displacing the block from ( x=3 ) to ( x=1 ) B. Positive in displacing the block from ( x=-3 ) to ( x=-1 ) c. Negative in displacing the block from ( x=0 ) to ( x=4 ) D. zero in displacing the block from ( x=-2 ) to ( x=+2 ) | 11 |

638 | A bullet of mass 20 g moving with a velocity of ( 500 mathrm{m} / mathrm{s} ), strikes a tree and goes out from the other side with a velocity of ( 400 mathrm{m} / mathrm{s} ). Calculate the work done by the bullet (injoules) in passing through the tree. ( mathbf{A} cdot 900 J ) B. ( 800 J ) c. ( 950 J ) D. ( 500 J ) | 11 |

639 | A solid sphere rolls without slipping on a rough horizontal floor, moving with a speed ( boldsymbol{v} . ) It makes an elastic collision with a smooth vertical wall. After impact, This question has multiple correct options | 11 |

640 | is said to be done only when the force applied on a body makes the body to move. A. work B. Momentum c. Retardation D. None of these | 11 |

641 | An overhead tank having some water possesses ( ldots ) mergy. A. Kinetic B. Potential c. Thermal D. Electrical | 11 |

642 | A wire suspended vertically from one of its ends is stretched by attaching a weight of ( 200 mathrm{N} ) to the lower end. The weight stretches the wire by 1 mm. Then the energy stored in the wire is A . 0.1 B. 0.2 c. 10 D. 20 | 11 |

643 | A system is provided 50 joule of heat and work done no the system is 10 J. The change in in iternal energy during the process is A . ( 40 mathrm{J} ) B. 60 J c. 80 D. 50 J | 11 |

644 | 16. The blocks A and B shown in Fig. 8.238 have masses MA = 5 kg and MB = 4 kg. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is 5 m 37° Fig. 8.238 | 11 |

645 | 68. Two constant forces É 2 act on a body of mass 8 kg. These forces displace the body from point P (1, 2, 3) to Q (2,3,7) in 2 s starting from rest. Force F, is of magnitude 9 N and is acting along vector (2î – 2j + k). Work done by the force F2 is a. 80J b. -80 J C. -180 J d. 180 J | 11 |

646 | toppr ( t ) Q Type your question- Which of the diagrams shown In ( (overline{4}) ) figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground? ( A ) B. ( c ) ( D ) | 11 |

647 | The coefficient of restitution (e) for a perfectly elastic collision is A . -1 B. ( c cdot alpha ) ( D ) | 11 |

648 | In a shotput event, an athlete throws the shotput of mass ( 10 k g ) with an initial speed of ( 1 m s^{1} ) at ( 45^{circ} ) from a height ( 1.5 m ) above ground. Assuming air resistance to be negligible and acceleration due to gravity to be ( 10 m s^{2} ) the kinetic energy of the shotput when it just reaches the ground will be: A . 2.5 .5 в. ( 5.0 J ) c. ( 52.5 J ) D. ( 155.0 J ) | 11 |

649 | A spring of force constant ( mathrm{k}=300 mathrm{N} / mathrm{m} ) connects two blocks having masses 2 kg and 3 kg, lying on a smooth horizontal plane. If the spring block system is released from a stretched position, find the number of complete oscillations in 1 minute. Take ( pi=sqrt{10} ) A .44 B. 150 ( c cdot 34 ) D. 55 | 11 |

650 | Kinetic energy of the liquid per unit mass is ( mathbf{A} cdot frac{1}{2} m v^{2} ) B ( cdot frac{1}{2} v^{2} ) C ( cdot frac{1}{2} m^{2} v ) D. ( m v^{2} ) | 11 |

651 | A 5 kg mass moving at a speed of ( 13 m s^{-1} ) collides head on with a body of mass ( 1 mathrm{kg} ) at rest, if they move with a common velocity after collision in the same direction, find the velocity? A ( cdot 103 mathrm{ms}^{-1} ) B . ( 10.83 mathrm{ms}^{-1} ) c. ( 1.03 mathrm{ms}^{-1} ) D. ( 20 mathrm{ms}^{-1} ) | 11 |

652 | Which one of the following statements does hold good when two balls of masses ( m_{1} ) and ( m_{2} ) undergo elastic collision? A. When ( m_{1}m_{2} ) and ( m_{2} ) at rest, after collision the ball of mass ( m_{2} ) moves with four times the velocity of ( m_{1} ) c. When ( m_{1}=m_{2} ) and ( m_{2} ) at rest, there will be maximum transfer of K.E D. When collision is oblique and ( m_{2} ) at rest with ( m_{1}=m_{2} ) after collision the ball moves in opposite direction | 11 |

653 | Statement A : A neutron travelling with a velocity collides head on an atom of atomic mass number ( A ) at rest. The fraction of the total energy retained by neutron is ( left(frac{A-1}{A+1}right)^{2} ) Statement B : The kinetic energy conserves during an elastic collision ( A cdot A ) and ( B ) are true B. A is true but B is false c. A is false but B is true D. A and B are false | 11 |

654 | 27. Work done by gravity to w.r.t. the conveyor belt is a. -mgh b. -= mgh 2 mgh d. None of above | 11 |

655 | The angle between the diagonals of a cube with edges of length 1 is: ( A cdot sin ^{-1}(1 / sqrt{3}) ) B . ( cos ^{-1}(1 / sqrt{3}) ) c. ( tan ^{-1}(1 / sqrt{3}) ) D. ( cot ^{-1}(1 / sqrt{3}) ) | 11 |

656 | The work done in dragging a stone of mass 100 kg up an inclined plane 1 in 100 through a distance of ( 10 mathrm{m} ) is: A . 100 J B. 980 J c. 9800 D. 98 J | 11 |

657 | A ball of mass ( 100 g ) is thrown with a speed of ( 15 mathrm{m} / mathrm{s} ). Calculate its kinetic energy. | 11 |

658 | A neutron moving with a certain kinetic energy collides head on with an atom of mass number A. The fractional kinetic energy retained by it is A ( frac{A-1}{A+1} ) ( ^{mathrm{B}}left(frac{A+1}{A-1}right)^{2} ) c. ( frac{A+1}{A-1} ) ( ^{D cdot}left(frac{A-1}{A+1}right)^{2} ) | 11 |

659 | Potential energy function describing the interaction between two atoms of a diatomic molecule is ( U(r)=frac{a}{r^{12}}-frac{b}{r^{6}} ) Force acting between them will be zero when the distance between them would be A B. ( quadleft(frac{b}{2 a}right)^{frac{1}{6}} ) ( left(frac{a}{b}right)^{frac{1}{6}} ) D. ( quadleft(frac{b}{a}right)^{frac{1}{6}} ) | 11 |

660 | Student A and student B sit in identical office chairs facing each other, as shown in figure. Student A is heavier than student B. Student A suddenly pushes with his feet. Which of the following statements related to momentum is correct? A. Momentum of A is greater than momentum of B. Momentum of A and B are equal but opposite in direction 9 mentum of of B is greater than momentum of D direction | 11 |

661 | A constant force acting on a body of mass ( 3.0 mathrm{kg} ) changes its speed from ( 2.0 mathrm{ms}^{-1} ) to ( 3.5 mathrm{ms}^{-1} ) in ( 25 mathrm{s} ). The direction of the motion of the body remains unchanged. What is the magnitude of the force (in newton)? A . 0.18 в. 0.36 c. 0.72 D. 0.24 | 11 |

662 | toppr Q Type your question. following graph best represents the relation between the force exerted by the table on the chain with time? (Assume that the fallen part immediately comes to rest after collision with table and does not form a heap) ( A ) 3 ( c ) D | 11 |

663 | Car ( X ) of mass 200 kg moving at ( 5 mathrm{m} / mathrm{s} ) collides with car Y of mass ( 300 mathrm{kg} ) moving in the same direction at ( 3 mathrm{m} / mathrm{s} ) After the collision they move off together. What is their common velocity just after the collision? A. ( 4.2 mathrm{m} / mathrm{s} ) B. ( 5.6 mathrm{m} / mathrm{s} ) ( c cdot 3.8 m / s ) D. ( 7.8 mathrm{m} / mathrm{s} ) | 11 |

664 | Calculate the work done in moving the object from ( x=2 ) to ( x=3 mathrm{m} ) from the given graph. | 11 |

665 | A marble going at a speed of ( 12 m s^{-1} ) hits another marble of equal mass at rest. If the collision is perfectly elastic. Find the velocity of the first after collision. A . 4 B. c. 2 D. 3 | 11 |

666 | A particle of mass ( 0.5 k g ) travels in a straight line with velocity ( boldsymbol{v}=boldsymbol{a} boldsymbol{x}^{3 / 2} ) where ( a=5 m^{-1 / 2} s^{-1} . ) What is the work done by the net force during its displacement from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{2 m} ? ) | 11 |

667 | A ball is dropped from a height ( 8 mathrm{m} ) on a smooth horizontal surface. If height attained by the ball after the second collision is ( 2 mathrm{m} ), then the coefficient of restitution is : A ( cdot frac{1}{4} ) B. ( frac{1}{2} ) c. 1 D. ( frac{1}{sqrt{2}} ) | 11 |

668 | A particle moves in ( x y ) plane. The position vector at any time ( t ) is ( vec{r}= ) ( left{(2 t) hat{i}+left(2 t^{2}right) hat{j}right} m . ) The rate of change of ( theta ) at time ( t=2 ) second (where ( theta ) is an angle which its velocity vector makes with positive ( x-a x i s) ) is: A ( cdot frac{2}{17} operatorname{rad} / s ) в. ( frac{1}{14} r a d / s ) c. ( frac{4}{7} ) rad ( / ) s D. ( frac{6}{5} ) rad ( / ) s | 11 |

669 | A light and a heavy body have equal kinetic energies. The light body has greater momentum. A. True B. False | 11 |

670 | In a one-dimensional collision between two identical particles ( boldsymbol{A} ) and ( boldsymbol{B} . boldsymbol{B} ) is stationary and ( A ) has momentum ( p ) before impact. During impact, ( B ) gives an impulse ( J ) to ( A ). Find the coefficient of restitution between ( A ) and ( B ? ) | 11 |

671 | The potential energy between two atoms in a molecule is given by, ( U_{(x)}=frac{a}{x^{12}}- ) ( frac{B}{X^{6}}, ) where a and b are positive constants and ( x ) is the distance between the atoms. The system is in stable equilibrium when – ( mathbf{A} cdot x=0 ) B ( cdot x=frac{a}{2 b} ) c. ( x=left(frac{2 a}{b}right)^{1 / 6} ) D. ( x=left(frac{11 a}{5 b}right) ) | 11 |

672 | A uniform rod is resting freely over a smooth horizontal plane. A particle moving horizontally strikes at one end of the rod normally and gets stuck. Then This question has multiple correct options A. the momentum of the particle is shared between the particle and the rod and remains conserved B. the angular momentum about the mid-point of the rod before and after the collision is equal C. the angular momentum about the centre of mass of the combination before and after the collision is equal D. the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle | 11 |

673 | Consider the following statements ( A ) and ( mathrm{B} ) and identify the correct answer: ( A: ln ) an elastic collision, if a body suffers a head on collision with another of same mass at rest, the first body comes to rest while the other starts moving with the velocity of the first one. ( B: ) Two bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities. A. A and B are true B. A and B are false c. A is true but B is false D. A is false but B is true | 11 |

674 | A block of mass ( 20 mathrm{kg} ) is slowly slid up on a smooth incline of inclination53 ( ^{o} ) by a person. Calculate the work done by the person in moving the block through a distance ( 4 mathrm{m}, ) if the driving force is ( (mathrm{a}) ) parallel to the incline and (b) in the horizontal direction. ( left[boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right] ) | 11 |

675 | 21. The kinetic energy K of a particle moving along a circle of radius R depends upon the distance s as K = as?. The force acting on the particle is 7112 82 a. 2a $ b. 2as 1+ asli c. 2as d. 2a | 11 |

676 | A man, of mass ( m ), standing at the bottom of the staircase, of height ( boldsymbol{L} ) climbs it and stands at its top. This question has multiple correct options A. Work done by all forces on man is equal to the rise in potential energy mgL B. Work done by all forces on man is zero c. work done by the gravitational force on man is mgL D. The reaction force from a step does not do work because the point of application of the force does not move while the force exists | 11 |

677 | 28. A massless platform is kept on a light elastic spring as shown in Fig. 8.231. When a particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle strikes the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m? 0.1 kg Fig. 8.231 b. 2.96 m c. 3.96 m a. 0.96 m d. 0.48 m | 11 |

678 | Kinetic energy is proportional to This question has multiple correct options A. velocity B. mass C . square of velocity D. acceleration | 11 |

679 | Two bodies of equal weight are kept at heights of ( h ) and ( 1.5 h ) respectively. The ratio of their P.E. is: ( A cdot 3: 2 ) B. 2: 3 c. 1: 1 D. None of these | 11 |

680 | A rocket is moving in a gravity free space with a constant acceleration of ( 2 m s^{-2}, ) along ( +x ) direction (see figure) The length of a chamber inside the rocket is ( 4 mathrm{m} ). A ball is thrown from the left end of the chamber in ( +x ) direction with a speed of ( 0.3 m s^{-1} ) relative to the rocket. At the same time, another ball is thrown in – ( x ) direction with a speed of ( 0.2 m s^{-1} ) from its right end relative to the rocket. The time in seconds when the two balls hit each other is ( A ) ( B .3 ) ( c ) ( D ) | 11 |

681 | A ball of mass ( 0.2 mathrm{kg} ) is thrown vertically upwards by applying a force by hand. If the hand moves ( 0.2 mathrm{m} ) while applying the force and the ball goes up to 2 in height further, find the magnitude of the force. Consider ( g=10 m / s^{2} ) ( A cdot 16 N ) B. 20 N c. 22 D. ( 180 mathrm{N} ) | 11 |

682 | State work energy theorem. Plot spring force ( F ) versus ( x ) and obtain the expression for elastic potential energy of spring. | 11 |

683 | A body moves through a distance of ( ^{prime} boldsymbol{m}^{prime} ) in the following different ways. In which case is the maximum work done? A. when pushed over an inclined plane B. when lifted vertically upward c. when pushed over smooth rollers D. when pushed on a plane horizontal surface | 11 |

684 | A glass ball collides with a smooth horizontal surface with a velocity ( a hat{i}- ) b ( hat{j} ). If the coefficient of restitution of collision be ( e, ) find the velocity of the ball just after the collision. | 11 |

685 | If the potential energy of two molecules is give by, ( U=frac{A}{r^{12}}-frac{B}{r^{6}} ) then at equilibrium position, its potential energy is equal to? A ( cdot frac{A^{2}}{4 B} ) B. ( -frac{B^{2}}{4 A} ) c. ( left(frac{2 A}{B}right)^{frac{1}{6}} ) D. 3A | 11 |

686 | A block of mass ( m ) is moving with a constant acceleration ( a ) on a rough horizontal plane. If the coefficient of friction between the block and ground is ( mu, ) the power delivered by the external agent in a time interval ( t ) from the beginning is equal to: A ( cdot m a^{2} t ) в. ( mu ) mgat ( mathbf{c} cdot mu m(a+mu g) g t ) D. ( m(a+mu g) a t ) | 11 |

687 | 6. In Fig. 8.301, shown all the surfaces are frictionless, and mass of the block is m = 100 g. The block and the wedge are held initially at rest. Now the wedge is given a horizontal acceleration of 10 ms? by applying a force on the wedge, so that the block does not slip on the wedge. Then find the work done in joules by the normal force in ground frame on the block in 1 s. 10 ms 2 Fig. 8.301 | 11 |

688 | A body of mass ( 6 mathrm{kg} ) is under a force of 6 N which causes displacement in it given by ( S=frac{t^{2}}{4} ) at where ‘t’ is time. The work done by the force in 2 s is: A . 12 B. 9 J c. 6 J D. 3 J | 11 |

689 | ( vec{A} ) and ( vec{B} ) are two vectors ( operatorname{given} vec{A}= ) ( 2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}+hat{j} . ) The magnitude of the component ( vec{A} ) along ( vec{B} ) is | 11 |

690 | Which is incorrect? ( mathbf{A} cdot K cdot E cdot propto(operatorname{moment} u m)^{2} ) B. ( K . E . propto(text {velocity})^{2} ) C. ( K . E . propto(operatorname{mas} s)^{2} ) D. ( K . E . propto ) mass | 11 |

691 | Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices. | 11 |

692 | A metal bullet moving at ( 400 mathrm{ms}^{-1} ) strikes on a tree trunk and get embedded inside it. Assuming total kinetic energy is converted to heat and ( 50 % ) of heat is absorbed by the bullet, find the increase in its temperature. (specific heat capacity of metal ( = ) ( 200 J k g^{-1} K^{-1} ) and bullet not melts | 11 |

693 | A vertical spring with force constant ( k ) is fixed on a table. A ball of mass ( mathrm{m} ) at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is ( ^{mathbf{A}} cdot m g(h+d)-frac{1}{2} k d^{2} ) B . ( m g(h-d)-frac{1}{2} k d^{2} ) c. ( m g(h-d)+frac{1}{2} k d^{2} ) D ( m g(h+d)+frac{1}{2} k d^{2} ) | 11 |

694 | On a smooth surface there are five identical equally spaced balls ( A, B, C, D ) and E present with initial velocities ( 10 mathrm{m} / mathrm{s},-5 mathrm{m} / mathrm{s}, 2 mathrm{m} / mathrm{s},-3 mathrm{m} / mathrm{s} ) ( 3 mathrm{m} / mathrm{s} ) respectively, Collision between any two ball assumed to be elasitc. Then after all possible collision which pair of balls will have same speed as of initial ( A cdot A & D ) B. B & ( c cdot c & D ) ( D cdot A & C ) | 11 |

695 | One end of a spring of natural length ( ell_{0}=0.1 mathrm{m} ) and spring constant ( mathrm{k}=80 ) N/m is fixed to the ground and other end is fitted with a smooth ring of mass ( mathbf{m}=2 mathrm{gm}, ) which is allowed to slide on a horizontal rod fixed at a height ( h= ) ( 0.1 mathrm{m} . ) Initially, the spring makes an angle of ( 37^{circ} ) with vertical when the system is released from rest. When the spring becomes vertical, | 11 |

696 | A ball falls on the ground from a height of ( 2.0 m ) and rebounds up to a height of 1.5 ( m . ) Find the coefficient of restitution | 11 |

697 | A particle of mass ( M, ) moving with a velocity ( u ) makes a head on collision with a particle of ( m ) initially at rest so that the final velocities are along the same line. If the collision is elastic and ( frac{M}{m}=k, ) then the final velocity of the second particle of mass ( boldsymbol{m} ) is : A ( frac{2 u}{1+k} ) В ( frac{2 k u}{1+k} ) c. ( frac{2 u}{1-k} ) D. ( frac{k M u^{2}}{2(1-k)} ) | 11 |

698 | Two particles of mass ( m ), constrained to move along the circumference of a smooth circular hoop of equal mass ( m ) are initially located at opposite ends of a diameter and given equal velocities ( v_{0} ) shown in the figure. The entire arrangement is located in gravity free space. Their velocityjust before collision is? ( A ) в. ( frac{sqrt{3}}{2} v_{0} ) c. ( frac{2}{sqrt{3}} v ) D. ( frac{sqrt{7}}{3} v_{0} ) | 11 |

699 | What is the speed of the proton when it is ( 8 A ) away from the nucleus? A ( cdot 1.85 times 10^{5} mathrm{ms}^{-1} ) В. ( 1.85 times 10^{4} m s^{-1} ) c. ( 1.85 times 10^{3} m s^{-1} ) D. ( 1.85 times 10^{2} mathrm{ms}^{-1} ) | 11 |

700 | Multiple Correct Answers Type Suppose two particles 1 and 2 are projected in vertical plane simultaneously. Their angles of projection are ( 30^{circ} ) and ( theta ) respectively, with the horizontal. Let they collide after a time ( t ) in air. Then This question has multiple correct options A ( cdot theta=sin ^{-1}(4 / 5) ) and they will have same speed just before the collision B . ( theta=sin ^{-1}(4 / 5) ) and they will have different speed just before the collision C . ( x<1280 sqrt{3}-960 m ) D. It is possible that the particles collide when both of them are at their highest point. | 11 |

701 | A body of mass 2 kg starts with an initial velocity ( 5 mathrm{m} / mathrm{s} ). If the body is acted upon by a time dependent force (F) as shown in the figure, then work done on the body in 20 s is | 11 |

702 | Work-energy theorem is valid in the presence of A. External forces only B. Internal forces onlhy c. conservative forces only D. All type of forces | 11 |

703 | The speed of the disc ( M ) is ( A cdot 0 ) B. ( frac{v_{0}}{2} ) ( c cdot frac{200}{sqrt{5}} ) ( D cdot v_{0} ) | 11 |

704 | An object of mass ( m ) is tied to a string of length ( l ) and a variable force ( F ) is applied on it which brings the string gradually at an angle ( theta ) with the vertical Find the work done by the force ( F ) A. ( m g l(1-cos theta) ) в. ( m g l(2-cos theta) ) c. ( _{m g l}left(1-frac{cos theta}{2}right) ) D ( cdot operatorname{mgl}left(2-frac{cos theta}{2}right) ) | 11 |

705 | U. 4VEA 50. Two identical blocks A and B are placed on two inclined planes as shown in Fig. 8.241. Neglect resistance and other friction. Fixed 1 Fixed h 21 – KM Fig. 8.241 Read the following statements and choose options. Statement I: The kinetic energy of A on sliding to I will be greater than the kinetic energy of B on sliding to 0. Statement II: The acceleration of A will be greater than acceleration of B when both are released on the inclined plane. Statement III: The work done by external agent to move the block slowly from position B to O is negative. a. Only statement I is true b. Only statement II is true c. Only I and III are true d. Only II and III are true | 11 |

706 | 4. The power exerted on the body at 2 s is a. 50 W b. 100 W c. 150 W d. 200 W | 11 |

707 | An object ( A ) of mass ( 1 k g ) is projected vertically upward with a speed of ( 20 m / s . ) At the same moment another object ( B ) of mass ( 3 k g, ) which is initially above the object ( A ), is dropped from a height ( h=20 m . ) The two point like objects ( (A text { and } B) ) collide and stick to each other. The kinetic energy is ( boldsymbol{K} ) (in ( boldsymbol{J} ) of the combined mass just after collision, find the value of ( boldsymbol{K} / mathbf{2 5} ) | 11 |

708 | Find the angle between ( overrightarrow{boldsymbol{A}}=mathbf{4} hat{mathbf{i}}+hat{mathbf{j}}+ ) ( mathbf{3} hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}+mathbf{3} hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}} ) | 11 |

709 | The work done in bringing three particles each of mass ( 10 g m ) from large distances to the vertices of an equilateral triangle of side ( 10 mathrm{cm} ) is A ( cdot 10^{-13} J ) ( J ) В. ( 2 times 10^{-13} mathrm{J} ) c. ( 4 times 10^{-11} J ) D. ( 10^{-11} J ) | 11 |

710 | P5 13. A charged particle X moves directly towards another charged particle Y. For the X plus Y system, the total momentum is p and the total energy is E. a. p and E are conserved if both X and Y are free to move. b. (a) is true only if X and Y have similar charges. c. If Y is fixed, E is conserved but not P. d. If Y is fixed, neither E nor P is conserved. | 11 |

711 | An elevator platform is going up at a speed ( 20 mathrm{ms}^{-1} ) and during its upward motion a small ball of 50 g mass falling in downward direction strikes the platform elastically at a speed ( 5 mathrm{ms}^{-1} ) Find the speed (in ( mathrm{ms}^{-1} ) ) with which the ball rebounds: | 11 |

712 | A cricket ball and a ping-pong ball are dropped from the same height in a vacuum chamber. When they have fallen half way down, they have the same: A. velocity B. potential energy c. kinetic energy D. rest energy | 11 |

713 | A particle of mass ( mathrm{m} ) is attached to one end of a massless spring of force constant ( mathrm{k}, ) lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time ( t=0 ) with an initial velocity ( u_{0} . ) When the speed of the particle is ( 0.5 u_{0} . ) It collides elastically with a rigid wall. After this collision. This question has multiple correct options A. The speed of the particle when it returns to its equilibrium position is ( u_{0} ) B. The time at which the particle passes through the equilibrium position for the first time is ( t=pi sqrt{frac{m}{k}} ) c. The time at which the maximum compression of the spring occurs is ( t=frac{4 pi}{3} sqrt{frac{m}{k}} ) D. The time at which the particle passes through the equilibrium position for the second time is ( t= ) ( frac{5 pi}{3} sqrt{frac{m}{k}} ) | 11 |

714 | Two particles ( A ) and ( B ) are moving with constant velocities ( v_{1} ) and ( v_{2} cdot A t t=0, v_{1} ) makes an angle ( theta_{1} ) with the line joining ( A ) and ( B ) and ( v_{2} ) makes an angle ( theta_{2} ) with the line joining ( A ) and ( B ). Find their velocity of approach | 11 |

715 | 34. A person of mass 70 kg jumps from a stationary helicopter with the parachute open. As he falls through 50 m height, he gains a speed of 20 ms. The work done by the viscous air drag is a. 21000 J b. -21000 J c. -14000 J d. 14000 J Abortiol, looted in one dimensional notential field hoe | 11 |

716 | A boy held a book of ( 1 mathrm{kg} ) at a height of 1 metre for 60 seconds. Calculate the work done : A . 60 J B. 30 J c. 15 J D. | 11 |

717 | A body of mass ( 300 mathrm{kg} ) is moved through ( 10 m ) along a smooth inclined plane of an angle ( 30^{circ} . ) The work done in moving the mass in joules is: ( left(g=9.8 m s^{-2}right) ) A. 9800 B. 14700 ( c .3450 ) D. 4900 | 11 |

718 | A rigid massless rod of length ( boldsymbol{L}=mathbf{1} boldsymbol{m} ) joins two particles each of mass ( m= ) 1 kg. The rod lies on a frictionless table, and is struck by a particle of equal mass ( m=1 k g ) and velocity ( v_{0}=7 sqrt{2} ) moving as shown in the figure. After the collision the partcle moves straight back. Calculate the angular velocity of mass after collision, assuming that collision is perfectly elastic. | 11 |

719 | A machine raises a load of ( mathbf{7 5 0} boldsymbol{N} ) through a height of ( 16 m ) in ( 5 s . ) Calculate energy spent by machine: A. ( 12000 k J ) в. ( 12 k J ) c. ( 1200 J ) D. ( 120 k J ) | 11 |

720 | A block of mass ( 0.5 k g ) is moving with a speed of ( 2.0 m / s ) on smooth surface. It strikes another mass of ( 1.0 k g ) and then they move together as a single body. The energy loss during collision is (in J) A . 0.16 B. 0.67 c. 1.0 D. 6.7 | 11 |

721 | A neutron moving with velocity u collides with a stationary ( boldsymbol{alpha}- ) particle The velocity of the neutron after collision is A. ( -frac{30}{5} ) в. ( frac{30}{5} ) c. ( frac{20}{5} ) D. ( -frac{2 U}{5} ) | 11 |

722 | A body freely falls from a certain height on to the ground in a time ( t . ) During the first one third of the time interval it gains a kinetic energy ( Delta k_{1} ) and during the last one-third of the interval, it gains a kinetic energy ( Delta k_{2} ). The ratio ( Delta k_{1} ) ( boldsymbol{Delta} boldsymbol{k}_{2} ) is: A . 1: 1 B. 1: 3 c. 1: 4 D. 1: 5 | 11 |

723 | A particle ( (boldsymbol{m}=mathbf{1} boldsymbol{k} boldsymbol{g}) ) slides down a frictionless rack (AOC) starting from rest at a point ( A ) (height ( 2 m ) ). After reaching ( C, ) the particle continuous to move freely in air as a projectile. When it reaching its highest point ( boldsymbol{P} ) (height 1 ( m ) ), the kinetic energy of the particle (in J) is : (Figure drawn is schematic and not to scale; take ( g=10 m s^{-2} ) | 11 |

724 | How far from the midpoint of the stick is the center of mass of the stick-puck combination after the collision? A. ( l ) ( overline{2} ) B. ( frac{l}{3} ) c. ( frac{l}{4} ) D. None of these | 11 |

725 | A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If ( e ) is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be: A ( cdot frac{(1-e)}{(1+e)} ) в. ( frac{(1+e)}{(1-e)} ) c. ( frac{(e-1)}{(e-1)} ) D. ( frac{(e+1)}{(e-1)} ) | 11 |

726 | The speed of an object of mass ( 2 k g ) increases from ( 2 m / s ) to ( 4 m / s ) in ( 3 s ) Find out the total work done on the object during this time interval? A . ( 4 J ) B. 6.5 c. ( 12 J ) D. 24J ह. ( 36 J ) | 11 |

727 | If object having total energy ( boldsymbol{E}_{1} ) is having the same ( P E ) curve as shown in the figure, then ( mathbf{A} cdot r_{0} ) is the maximum distance of the object from the earth’s centre B. the object and the earth system is bounded one C. the ( K E ) of the object is zero when ( r=r_{0} ) D. all the above | 11 |

728 | A man carries a load on his headd through distance of ( 5 mathrm{m} ). The maximum amount of work done when he A. Move it over an inclined plane B. Moves it over a horizontal surface c. Lifts it vertically upwardd D. None of these | 11 |

729 | A man throws the bricks to the height of ( 12 m ) where they reach with a speed of ( 12 m / s . ) If he throws the bricks such that theyjust reach this height, then what percentage of energy will he save? A . ( 19 % ) B. 38% c. ( 57 % ) D. 76% | 11 |

730 | 14. Find how much mass m will rise if 4 m falls away. Blocks are at rest and in equilibrium. m 4m Fig. 8.218 | 11 |

731 | The graph above shows the magnitude of the force applied to an initially stationary ( 20 k g ) curling rock over time. Find out the velocity of the rock after the force has been applied to it? A ( .1 .25 mathrm{m} / mathrm{s} ) в. ( 5 m / s ) ( mathrm{c} cdot 10 mathrm{m} / mathrm{s} ) D. ( 25 m / s ) E. ( 50 m / s ) | 11 |

732 | Work-energy theorem is valid in the presence of A. All types of forces B. Internal force only c. conservative forces only D. Non-conservative forces only | 11 |

733 | 6. A force F = -K (yi + xj) (where K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a,0), and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particle is (IIT JEE, 1998) a. -2Ka? b. 2Ka? c. -Ka? d. Ka? | 11 |

734 | The angle between two vectors ( vec{A}= ) (4,-2,5) and ( vec{B}=(3,1,-2) ) is: A ( cdot 60^{circ} ) в. ( 30^{circ} ) ( c cdot 90^{0} ) D. ( 45^{circ} ) | 11 |

735 | 14. The potential energy o, in joule, of a particle of mass 1 kg, moving in the x-y plane, obeys the law o = 3x + 4y, where (x, y) are the coordinates of the particle in metre. If the particle is at rest at (6,4) at time t = 0, then a. The particle has constant acceleration. b. The work done by the external forces, the position of rest of the particle and the instant of the particle crossing the x-axis is 25 J. c. The speed of the particle when it crosses the y-axis is 10 ms. d. The coordinates of the particle at time t = 4 s are (-18, -28) | 11 |

736 | ( mathbf{A} ) ( 0.5 mathrm{kg} ) block slides from the point ( mathrm{A} ) on a horizontal track with an initial speed ( 3 mathrm{m} / mathrm{s} ) towards a weightless horizontal spring of length ( 1 mathrm{m} ) and force constant 2 N/m. The part AB of the Track is frictionless and the part BC has the coefficient of static and kinetic friction as 0.22 and 0.20 respectively. If the distance ( A B ) and ( B D ) are ( 2 m ) and 2.14 m respectively, find the total distance through which the block moves before it comes to rest completely. ( left(g=10 m / s^{2}right) ) | 11 |

737 | An artificial satellite of mass ( m ) is moving in circular orbit at a height equal to the radius ( R ) of the earth. Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One part of the satellite stops just after the explosion. The increase in the mechanical energy of the system due to explosion will be (Given: acceleration due to gravity on the surface of earth is ( g ) ) A. ( m g R ) в. ( frac{m g R}{2} ) c. ( frac{m g R}{4} ) D. ( frac{3 m g R}{4} ) | 11 |

738 | A block of mass ( m ) is projected with velocity ( u ) forwards another identical block with has a massless spring attached to its face. The spring constant of the spring is ( k ) and blocks are on smooth horizontal surface. Maximum compression in the spring is: | 11 |

739 | If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k} . ) Then, the value of ( alpha ) is : A ( cdot frac{-1}{2} ) B. – – ( c cdot frac{1}{2} ) D. 1 | 11 |

740 | A ball is thrown at an angle of incidence ( boldsymbol{theta}^{prime} ) on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other if the coefficient of restitution is ‘e’ then’ ( theta ) ‘is equal to A ( cdot tan ^{-1}(e) ) B ( cdot tan ^{-1}(2 e) ) c. ( tan ^{-1}(sqrt{2} e) ) D. ( tan ^{-1}(sqrt{e}) ) | 11 |

741 | Two inclined friction less tracks, one gradual and the other steep meet at ( boldsymbol{A} ) from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given ( boldsymbol{theta}_{mathbf{1}}= ) ( mathbf{3 0}^{0}, boldsymbol{theta}_{2}=mathbf{6 0}^{0}, ) and ( boldsymbol{h}=mathbf{1 0} boldsymbol{m}, ) what are the speeds and times taken by the two stones ? | 11 |

742 | A body of mass ( 4 mathrm{kg} ) moving with a velocity of ( 9 mathrm{m} / mathrm{s} ). Collides with a body of ( 8 mathrm{kg} ) at rest. The coefficient of restitution is ( 0.33 . ) After collision the velocity of body having mass ( 4 mathrm{kg} ) is: ( A cdot 1 mathrm{m} / mathrm{s} ) B. ( 4 mathrm{m} / mathrm{s} ) ( c cdot 3 m / s ) D. ( 9 mathrm{m} / mathrm{s} ) | 11 |

743 | A ball dropped from a ( 20 m ) height loses ( 40 % ) of its energy on hitting the ground. Upto what height does the ball rebound? ( A cdot 28 m ) в. ( 8 m ) ( c .12 m ) D. 20m | 11 |

744 | A plastic ball falls from a height of 4.9 metre and rebounds several times from the floor. What is the coefficient of restitution during the impact with the floor if 1.3 seconds pass from the first impact to the second one? A . 0.9 B. ( 0 . ) ( c .0 .7 ) D. 0.8 | 11 |

745 | Work done by centripetal force in revolving a satellite around the earth is A . zero B. unity c. infinity D. nothing can be decided | 11 |

746 | A ride in an amusement park called scream machine swings the riders around a complete vertical circle during the course of the ride. Identify where on the ride both PE and KE are equal? A. Point ( A ) B. Point B c. Point ( C ) D. Point D E . Point E | 11 |

747 | Which one of the following energies cannot be possessed by a body at rest? A. Potential energy B. Kinetic energy C. Thermal energy D. Magnetic energy | 11 |

748 | toppr Q Type your question the following graphs violates the law of conservation of energy? 3 ( c ) ( D ) | 11 |

749 | If ( g ) is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( boldsymbol{m} ) raised from the surface of the earth to a height equal to the radius ( R ) of the earth is A. ( 2 m g R ) в. ( frac{1}{2} m g R ) c. ( frac{1}{4} m g R ) D. ( m g R ) | 11 |

750 | A gravitational field is present in a region. A point mass is shifted from ( boldsymbol{A} ) to ( B, ) along different paths shown in the figure. If ( W_{1}, W_{2} ) and ( W_{3} ) represent the work done by gravitational force for respective paths, then ( mathbf{A} cdot W_{1}=W_{2}=W_{3} ) В. ( W_{1}>W_{2}>W_{3} ) c. ( W_{1}>W_{3}>W_{2} ) D. none of these | 11 |

751 | 31. The ratio of magnitude of work done by camel on the load during accelerated motion to retarded motion is a. 3:5 b. 2.2:1 c. 1:1 d. 5:3 | 11 |

752 | A ( 0.098-k g ) block slides down a frictionless track as shown in Fig. The time taken by the block to move from ( A ) to ( B ) is: ( ^{A} cdot frac{1}{sqrt{g}} ) в. ( frac{2}{sqrt{g}} ) c. ( frac{3}{sqrt{g}} ) D. ( frac{4}{sqrt{g}} ) | 11 |

753 | If a ship of mass ( 4 times 10^{7} ) kg initially at rest is pulled by a force of ( 5 times 10^{4} mathrm{N} ) through a distance of 4 m, then the speed of the ship will be (resistance due to water is negligible) ( mathbf{A} cdot 5 m s^{-1} ) B . ( 1.5 mathrm{ms}^{-1} ) ( mathrm{c} cdot 60 mathrm{ms}^{-1} ) D. ( 0.1 mathrm{ms}^{-1} ) | 11 |

754 | A particle of mass ( m ) moving in ( x ) direction with speed ( 2 v ) is hit by another particle of mass ( 2 m ) moving in the ( y ) direction with speed ( v ). If the collisioni is perfectly inelastic, the percentage of the energy retained by the colliding particles after the collision is close to A . ( 56 % ) B. 80% c. ( 35 % ) D. 44% | 11 |

755 | A body dropped freely from a height h onto a horizontal plane, bounces up and down and finally comes to rest. The coefficient of restitution is e, the ratio of distance travelled in two consecutive rebounds A ( .1: e ) B . ( e: 1 ) ( mathbf{c} cdot 1: e^{2} ) D. ( e^{2}: 1 ) | 11 |

756 | Two protons are brought nearer; what will be the effect on potential energy of system? | 11 |

757 | The maximum vertical distance through which a fully dressed astronaut canjump on the earth is ( 0.5 mathrm{m} ). If mean density of the moon is two thirds that of the earth and radius is one quarter that of the earth, the maximum vertical distance through which he can jump on the moon and the ratio of time of duration of the jump on the moon to that on the earth are. A. ( 3 mathrm{m}, 6: ) в. 6 m, 3: ( c cdot 3 m, 1: 6 ) D. ( 6 mathrm{m}, 1: 6 ) | 11 |

758 | If ( n ) balls hit elastically and normally on a surface per unit time and all the balls are of mass ( m ) moving with the same velocity ( u, ) then force on the surface is: ( mathbf{A} cdot m times u times n ) В . ( 2 times m times u times n ) c. ( frac{1}{2} times m u^{2} n ) D. ( m u^{2} n ) | 11 |

759 | Statement 1: The scalar product of two vector can be zero. Statement 2:If two vector are perpendicular to each other, their scalar product will be zero. A ( cdot ) a) Statement- -1 is false, statement- 2 is true B. b) Statement-1 is true, Statement-2 is true, Statement 2 is a correct explanation for statement- c. c) Statement- – is true, Statement-2 is true; Statement 2 is not a correct explanation for statement- D. d) Statement-1 is true, Statement-2 is false | 11 |

760 | An vehicle has a mass of 1500 kg. What must be the force between the vehicle and the road if the vehicle is to be stopped with a negative acceleration of ( 1.7 m s^{-2} ? ) A. ( 2550 N ) in a direction opposite to that of the vehicle B. ( 2550 N ) in a direction same to that of the vehicle c. ( 1550 N ) in a direction opposite to that of the vehicle D. ( 1550 N ) in a same opposite to that of the vehicle | 11 |

761 | A boy is moving on a straight road against a frictional force of ( 5 N . ) After travelling a distance of ( 1.5 k m, ) he forgets the correct path at a round about (see fig.) of radius ( 100 m ) However, he moves on the circular path for one and half cycle and then he moves forward upto ( 2.0 k m . ) Calculate the work done by him ( (pi=3.14) ) | 11 |

762 | The potential energy of an object of a mass m moving in xy plane in a conservative field is given by U=ax+by, where ( x ) and ( y ) are position coordinates of the object. Find magnitude of acceleration :- A ( cdot frac{sqrt{a^{2}+b^{2}}}{2 m} ) ( ^{text {В } cdot frac{a^{2}+b^{2}}{m}} ) c. ( sqrt{a^{2}+b^{2}} ) D. None | 11 |

763 | When the load on a wire is slowly increased from 3 to ( 5 k g w t ), the elongation increases from 0.61 to 1.02 ( m m ). The work done during the extension of wire is ( mathbf{A} cdot 0.16 J ) в. ( 0.016 J ) c. 1.6 .5 D. 16.5 | 11 |

764 | Illustration 8.46 A body of mass m hangs by an inextensible string that passes over a smooth mass less pulley that is fitted with a light spring of stiffness k as shown in Fig. 8.99. If the body is released from rest and the spring is released, calculate the maximum elongation of the spring Fig. 8.99 | 11 |

765 | A moving block having mass ( m ), collides with another stationary block having mass ( 4 m . ) The lighter block comes to rest after collision. When the initial velocity of the lighter block is ( v ), then the value of coefficient of restitution ( (e) ) will be: A . 0.5 B. 0.25 c. 0.4 D. 0.8 | 11 |

766 | The velocity of a body moving in a straight line is increased by applying a constant force ( F ) for some distance in the direction of the motion. The increase in the kinetic energy of the body is equal to A. the potential energy of the body. B. the work done by the force on the body. c. the momentum of the body. D. the torque on the body. | 11 |

767 | 76. A particle of mass m slides along a curved-flat-curved track. The curved portions of the track are smooth. If the particle is released at the top of one of the curved portions. the particle comes to rest at flat portion of length I and of 1 Minette after covering a distance of Fig. 8.254 b. _H_ 31 2U kinetic Mkinetic | 11 |

768 | A object of mass ( 40 k g ) having velocity ( 4 m / s ) collides with another object ( m= ) ( 60 k g ) having velocity ( 2 m / s . ) The collision is perfectly inelastic. The loss in energy is A . ( 110 J ) в. ( 48 J ) ( mathrm{c} .3925 ) D. ( 440 J ) | 11 |

769 | 4. A body is attached to a spring whose other end is fixed. If the spring is elongated by x, its potential energy is U= 5×2, where x is in metre and U is in joule. U-x graph is V (c) (d) | 11 |

770 | A sphere of mass ( m ) is moving with a velocity ( (4 hat{i}-hat{j}) m / s ) hits a surface and rebounds with a velocity ( (hat{i}+3 hat{j}) m / s . ) The coefficient of restitution between the sphere and the surface is ( k / 16 . ) find the value of ( k ) ( A cdot 9 ) B. 8 ( c cdot 7 ) D. 6 | 11 |

771 | A particle has potential energy dependent on its position on the ( x ) axis, represented by the function ( U(x)= ) ( e^{2 x}+1 ) for all real values of ( x ) where ( U(x) ) and ( x ) are given in standard units. The force it feels at position ( x=1 ) is closest to A. ( 7.39 N ) B. ( 8.39 N ) c. ( -8.39 N ) D. ( 14.8 N ) E. ( -14.8 N ) | 11 |

772 | If a vector ( vec{A} ) makes an angles ( alpha, beta ) and ( Y ) respectively with the ( x, y ) and ( z ) axes respectively. Then ( sin ^{2} alpha+sin ^{2} beta ) ( +sin ^{2} gamma ) is equal to ( mathbf{A} cdot mathbf{0} ) B. 1 c. 2 D. 3 | 11 |

773 | What is the velocity of the cart just after the first collision? A ( cdot frac{-m v_{0}}{m+M} ) в. ( frac{M v_{0}}{m+M} ) c. ( frac{M-m}{M+m} v_{0} ) D. ( frac{2 M}{m+M} v_{0} ) | 11 |

774 | A bullet of mass 125 gm leaves a rifle with a velocity of ( 500 m s^{-1} ). The rifle recoils with a velocity of ( 5 m s^{-1} ). Find the mass of the rifle. ( A cdot 100 mathrm{kg} ) B. 12.5 kgg ( c cdot 1.25 mathrm{kg} ) D. 125 kg | 11 |

775 | A sphere rolling on a horizontal rough surface collides elastically with a smooth vertical wall, as shown in Figure. State which of the following statements is true or false. After collision the friction the linear | 11 |

776 | A body of mass ( 10 g m ) moving with a velocity of ( u_{1} c m / s ) collides with a stationary mass of ( 90 g ) m. The collision is perfectly elastic. Find the percentage loss of kinetic energy of the first body. A . 36 B . 48 c. 64 D. | 11 |

777 | Two identical balls are projected, one vertically up and the other at an angle of ( 30^{0} ) to the horizontal, with same initial speed. The potential energy at the highest point is in the ratio: A . 4: 3 B. 3: ( c cdot 4: ) D. 1: | 11 |

778 | Which of the following graphs closely represents the kinetic energy ( (K) ) of a freely falling body and its height ( (h) ) above the ground? ( A ) в. c. D. | 11 |

779 | The volume of a colloidal particle ( V_{c} ) as compared to the volume of a solute particle in atrue solution ( V_{s} ) could be A ( cdot frac{V_{c}}{V_{s}}=1 ) B. ( frac{V_{c}}{V_{s}}=10^{23} ) c. ( frac{V_{c}}{V_{s}}=10^{-3} ) D. ( frac{V_{c}}{V_{s}}=10^{3} ) | 11 |

780 | An object of mass ( m ) and velocity ( v_{0} ) strikes a rigid uniform rod of length ( l ) and mass ( m_{r} . ) The rod is hanging by a frictionless pivot from the ceiling. Immediately after striking the rod, the object continues forward but its speed reduces to ( frac{v_{0}}{2} . ) The moment of inertia of the rod about its centre of mass is ( I_{C M}=frac{1}{2} m_{r} l^{2} . ) For the collision to be inelastic: A. the rod and object are of equal mass B. the rod is either heavier or lighter than the object c. the rod is of negligible mass D. none of these | 11 |

781 | A block moving in air breaks into two parts and the parts separate: This question has multiple correct options A. the total momentum must be conserved B. the total kinetic energy must be conserved C. the total momentum must change D. the total kinetic energy must change | 11 |

782 | Two particles of mass ( M_{A} ) and ( M_{B} ) and there velocities are ( V_{A} ) and ( V_{B} ) respectively collides. After collision they inter changes their velocities then ratio of ( frac{boldsymbol{M}_{boldsymbol{A}}}{boldsymbol{M}_{boldsymbol{B}}} ) is: A ( cdotleft(text { a) } frac{V_{A}}{V_{B}}right. ) в. (b) ( frac{V_{B}}{V_{A}} ) c. (c) ( frac{V_{A}+V_{B}}{V_{B}-V_{A}} ) D. (d) | 11 |

783 | The resultant of two forces, one double then other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is ( A cdot 120^{circ} ) B. 60 ( c cdot 90 ) D. 150 | 11 |

784 | A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy? | 11 |

785 | Two particles of masses ( m ) and ( 2 m ) moving in opposite directions collide elastically with velocity ( 2 nu ) and ( nu ) respectively. Find their velocities after collision. [ n stackrel{2 v}{longrightarrow} quad stackrel{v}{-2 m} ] | 11 |

786 | Calculate the height through which a body of mass ( 0.5 k g ) is lifted if the energy spent in doing so is ( 1.0 J . ) (Take ( boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-2} mathbf{)} ) ( A cdot 2 m ) в. ( 0.2 m ) ( c .20 m ) D. ( 0.4 m ) | 11 |

787 | Three blocks are initially placed as shown in the figure. block ( A ) has mass ( m ) and initial velocity ( v ) to the right. Block ( B ) with mass ( m ) and block ( C ) with mass ( 4 m ) are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block ( boldsymbol{A} ) is : A. ( 0.6 v ) to the left B. ( 1.4 v ) to the left ( c . v ) to the left D. ( 0.4 v ) to the right | 11 |

788 | A ball falls vertically onto a floor with momentum ( p ) and then bounces repeatedly, the coefficient of restitution is ( e . ) The total momentum imparted by the ball to the floor is A ( cdot rho(1+e) ) B. ( frac{1}{1-e} ) ( ^{c} rholeft(frac{1+e}{1-e}right) ) ( ^{mathrm{D}} rholeft(1-frac{1}{e}right) ) | 11 |

789 | Calculate the work required to be done to stop a car of ( 1500 mathrm{kg} ) moving at a velocity of ( 60 mathrm{km} / mathrm{h} ? ) | 11 |

790 | A ball falls freely under gravity from rest. Name the kind of energy it will possess at the point from where it falls: A. Maximum energy B. Heat energy c. Potential energy D. Kinetic energy | 11 |

791 | The angle between force ( overrightarrow{boldsymbol{F}}=(mathbf{3} hat{boldsymbol{i}}+ ) ( 4 hat{j}-5 hat{k}) ) unit and displacement ( overrightarrow{boldsymbol{d}}= ) ( (5 hat{i}+4 hat{j}+3 hat{k}) ) unit is ( A cdot cos ^{-1}(0.16) ) B. ( cos ^{-1}(0.32) ) ( mathbf{c} cdot cos ^{-1}(0.24) ) D ( cdot cos ^{-1}(0.64) ) | 11 |

792 | Energy required to move a body of mass ( mathrm{m} ) from an orbit of radius ( 2 mathrm{R} ) to ( 3 mathrm{R} ) is: ( ^{mathbf{A}} cdot frac{G M m}{12 R^{2}} ) в. ( frac{G M m}{3 R^{2}} ) c. ( frac{G M m}{8 R} ) D. ( frac{G M m}{6 R} ) | 11 |

793 | A boy is swinging on a swing such that his lowest and highest position are at heights of ( 2 m ) and ( 4.5 m ) respectively. His velocity at the lowest position is A ( .2 .5 m s^{-} ) B. ( 7 m s^{-1} ) ( mathrm{c} cdot 14 mathrm{ms}^{-1} ) D. ( 20 m s^{-1} ) | 11 |

794 | Mass ( m_{1} ) strikes ( m_{2} ) which is at rest. The ratio of masses for which they will collide again is : (Collisions between ball and wall are elastic. Coefficient of restitution between ( m_{1} ) and ( m_{2} ) is ( e ) and all the surfaces are smooth A ( cdot frac{e}{2+e} ) B. ( frac{2 e}{2+e} ) ( c ) ( D ) | 11 |

795 | In which of the following work is being done? This question has multiple correct options A. Man sitting on a bench B. Person Standing with a basket of fruit on the head. c. Climbing a tree to pluck D. Pushing a wheelbarrow of bricks. | 11 |

796 | 3. The PE of a certain spring when stretched from natural length through a distance 0.3 m is 5.6 J. Find the amount of work in joule that must be done on this spring to stretch it through an additional distance 0.15 m. | 11 |

797 | Q Type your question vertical position and touching a block of mass ( M ) which is a rest on a horizontal surface. The rod is given a slight jerk and it starts rotating about point ( boldsymbol{O} ) This causes the block to move forward as shown. The rod loses contact with the block at ( boldsymbol{theta}=mathbf{3 0}^{circ} ) All surfaces are smooth. Now answer the following questions. The velocity of block when the rod loses contact with the block is A ( cdot frac{3 g l}{4} ) B. ( frac{5 g l}{4} ) c. ( frac{6 g l}{4} ) D. ( frac{7 g l}{4} ) | 11 |

798 | The distance AC is : A . ( 20 mathrm{m} ) B. 30 ( m ) ( c cdot 40 m ) D. ( 50 mathrm{m} ) | 11 |

799 | mole 8.1 Figure 8.167 a smooth circular path of radius on the horizontal plane which is quarter of a circle A block mass m is taken from position A to B under the action of a constant force F. Calculate the work done by force F. a. If it is always directed horizontally b. If the block is pulled by a force F which is always tangential to the surface Block is pulled with a constant force F which is always directed towards the point B | 11 |

800 | Two bars of masses ( m_{1} ) and ( m_{2} ) connected by a weightless spring of stiffness ( kappa ) (figure shown above) rest on a smooth horizontal plane. Bar 2 is shifted a small distance ( x ) to the left and then released. If the velocity of the centre of inertia of the system after bar breaks off the wall is given as ( v_{c m}= ) ( frac{s x sqrt{m_{2} k}}{left(m_{1}+m_{2}right)} . ) Find ( s ) | 11 |

801 | At what value of ( eta ) will the velocity of the disc after the collision be equal to zero? A. ( eta=4 ) В . ( eta=5 ) ( mathbf{c} cdot eta=6 ) D. ( eta=7 ) | 11 |

802 | A man of mass ( mathrm{m} ) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h. ( W_{text {gravity}}= ) work done by gravity on the man. ( W_{text {friction}}= ) work done by gravity on the man. ( W_{text {man}}= ) work done by man If in the previous problem, we replace the man by a block of mass ( mathrm{m} ) and release it from top of the inclined plane, and let it gain a speed ( v, ) then This question has multiple correct options A ( cdot W_{f r i c t i o n}=-m g h+frac{1}{2} m v^{2} ) B. ( W_{text {gravity}}=-m g h ) C. ( W_{text {friction}}=0 ) D. ( W_{text {friction}}=-mu g x, ) where ( x ) is the horizontal distance covered and ( mu ) is the coefficient of friction between the block and the ground | 11 |

803 | A force of 500 dyne acts on an object where the object moves through ( 8 m ) in the direction of force. Calcualate the work done in this case | 11 |

804 | A ( 20 mathrm{kg} ) object is lifted through a height of ( _{-1}-ldots- ) m when 784 J of work is done on it. [Assume ( left.boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2}right] ) ( A cdot 2 ) B. 4 c. 7.84 D. 3.92 | 11 |

805 | What is the projection of ( vec{P} ) on ( vec{Q} ? ) A ( . vec{Q} . vec{P} ) в. ( hat{P} . hat{Q} ) c. ( vec{P} . vec{Q} ) D. ( vec{P} . hat{Q} ) | 11 |

806 | Given: ( vec{a} ) and ( vec{b} ) are unit vector, and ( theta ) be the angle between them. Then ( frac{1-vec{a} cdot vec{b}}{1+vec{a} cdot vec{b}}= ) A ( cdot sin ^{2} frac{theta}{2} ) в. ( cos ^{2} frac{theta}{2} ) c. ( tan ^{2} frac{theta}{2} ) D. ( cot ^{2} frac{theta}{2} ) | 11 |

807 | The position function of a particle is given by ( boldsymbol{x}(t)=boldsymbol{k} boldsymbol{t}^{5 / 2}, ) where ( boldsymbol{k} ) is a constant. If the particle starts at rest and is propelled through some distance ( d ) so that the trajectory matches ( x(t), ) the work done on the particle is proportional to which power of ( t ? ) ( mathbf{A} cdot t^{5} ) B ( cdot t^{3} ) ( mathbf{c} cdot t^{5 / 2} ) ( mathbf{D} cdot t^{3 / 2} ) E. Not enough information | 11 |

808 | A bullet of mass 10 g moving with velocity of ( 1.5 mathrm{m} / mathrm{s} ) hits a thick wooden plank of mass 90 g. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank and both move with a certain speed. Calculate the speed with which plank containing the bullet moves? A. ( 0.15 mathrm{m} / mathrm{s} ) B. ( 0.5 mathrm{m} / mathrm{s} ) ( c cdot 1.5 mathrm{m} / mathrm{s} ) D. ( 2 mathrm{m} / mathrm{s} ) | 11 |

809 | A hammer of mass ( M ) falls from a height ( h ) repeatedly to drive a pile of mass ( m ) into the ground. The hammer makes the pile penetrate in the ground to a distance ( d ) in single blow. Opposition to penetration is given by: | 11 |

810 | n after hitting ing the collision 18. A tennis ball is dropped on a horizontal smooth sure It bounces back to its original position after b the surface. The force on the ball during the col is proportional to the length of compression of ball. Which one of the following sketches desc the variation of its kinetic energy K with time t le t most appropriately? The figures are only illustrative and not the scale. a. K b. K d. K | 11 |

811 | A bullet weighing 10 g is fired with a velocity of ( 800 m s^{-1} . ) After passing through a mud wall ( 1 mathrm{m} ) thick, its velocity decreases to ( 100 m s^{-1} ). Find the average resistance offered by the mud wall. | 11 |

812 | Two identical balls ( A ) and ( B ) are released from the position shown in Fig. 1.205. They collide elastically with each other on the horizontal portion. The ratio of heights attained by ( A ) and ( B ) after collision is (neglect friction) ( A cdot 1: 4 ) в. 2: 1 ( c .4: 13 ) D. 2: 5 | 11 |

813 | A uniform metal sphere of radius ( boldsymbol{R} ) and mass ( m ) is surrounded by a thin uniform spherical shell of same mass and radius ( 4 R ) The centre of the shell ( C ) falls on the surface of the inner sphere. Find the gravitational fields at points ( A ) and B. | 11 |

814 | 23. An object of mass m slides down a hill of arbitrary shape and after travelling a certain horizontal path stops because of friction. The total vertical height descended is h. The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion. The work that a tangential force must perform to return the object to its initial position along the same path is a. mgh b. – mgh c. -2mgh d. 2mgh | 11 |

815 | Given unit vectors ( overline{boldsymbol{m}}, overline{boldsymbol{n}} ) and ( overline{boldsymbol{p}} ) such that angle between ( bar{m} ) and ( bar{n}= ) angle between ( bar{p} ) and ( (bar{m} times bar{n})=pi / 6 ) then ( [overline{boldsymbol{n}} overline{boldsymbol{p}} overline{boldsymbol{n}}]= ) A. ( sqrt{3} / 4 ) B. 3/4 ( c cdot 1 / 4 ) D. none | 11 |

816 | A chain of mass ( mathrm{m} ) and length Lis over hanging from the edge of a smooth horizontal table such that ( frac{1}{n} ) of its length is lying on the table. The work done in pulling the chain completely on to the table is A ( cdot frac{m g L}{2 n^{2}} ) в. ( frac{m g L(n-1)^{2}}{2 n^{2}} ) c. ( frac{m g L(n-1)^{2}}{n^{2}} ) D. ( frac{m g L}{n^{2}} ) | 11 |

817 | A ( 1 mathrm{kg} ) block situated on a rough incline is connected to a spring of spring constant 100Nm-1100Nm-1 as shown The block is released from rest with the spring in the unstretched position. The block moves ( 10 mathrm{cm} ) down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless. | 11 |

818 | A body moves from point ( A ) and ( B ) under the action of a force, varying in magnitude as shown in figure below. Obtain the work done. Force is expressed in newton and displacement is in metre | 11 |

819 | The work done in holding 15 kg suitcase while waiting for a bus for 45 minutes is : ( A cdot 675 J ) B. 40500 c. 4500 D. zero | 11 |

820 | A particle hanging from a massless spring stretches it by ( 2 mathrm{cm} ) at earths surface. How much will the same particle stretch the spring at a height of ( 2624 mathrm{km} ) from the surface of the earth? (Radius of earth ( =6400 mathrm{km} ) ). A ( .1 mathrm{cm} ) B. ( 2 mathrm{cm} ) ( mathrm{c} .3 .3 mathrm{cm} ) D. 4 cm | 11 |

821 | A smooth sphere (mass ( 10 mathrm{kg} ) negligible radius) moves on a smooth curved surface from the point with a speed of ( 10 mathrm{m} / mathrm{s} ) as shown in figure. The sphere reaches the point D passing through point B. If the ground is taken as reference, Then ( left[boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right] ) This question has multiple correct options A. The total mechanical energy of the sphere at point A is zero B. The total mechanical energy of the sphere at the point A is 2500 J C. The kinetic energy at point B is 2500 J D. The notential energy at point B is 0 J | 11 |

822 | A man standing on the edge of the terrace of a high rise building throws a stone, vertically up with a speed of 20 ( mathrm{m} / mathrm{s} . ) Two seconds later, an identical stone is thrown vertically downwards with the same speed of ( 20 mathrm{m} / mathrm{s} ). Then : This question has multiple correct options A. the relative velocity between the two stones remains constant till one hits the ground B. both will have the same kinetic energy, when they hitt the ground c. the time interval between their hitting the ground is 2 s D. if the collision on the ground is perfectly elastic, both will rise to the same height above the ground | 11 |

823 | Two bullets ( P ) and ( Q ), masses 10 and 20 g, are moving in the same direction towards a target with velocities of 20 and ( 10 mathrm{m} / mathrm{s} ) respectively. Which one of the bullets will pierce a greater distance through the target? ( A cdot P ) B. c. Both will cover the same distance D. Nothing can be decided | 11 |

824 | The vector ( hat{i}+x hat{j}+3 hat{k} ) is rotated through an angle ( theta ) and doubled in magnitude,then it becomes ( 4 hat{i}+(4 x- ) 2)( hat{j}+2 hat{k} . ) The value of ( x ) are A ( cdot-frac{2}{3}, 2 ) в. ( frac{1}{3}, 2 ) c. ( frac{2}{3}, 2 ) D. zero, 2 | 11 |

825 | In which of the following cases, is the work done maximum? ( A ) B. ( mathbf{c} ) D. | 11 |

826 | A uniform stationary sphere starts rolling down from the upper end of the surface as shown in the figure, and it reaches the lower right end. Given, ( boldsymbol{H}= ) ( 27 m ) and ( h=20 m . ) The sphere will fall on the ground level at the following distance from ( C . ) (Assume horizontal projection) ( A cdot 12 m ) B. ( 24 m ) ( c .36 m ) D. 48 m | 11 |

827 | A 2 kg mass moving on a smooth frictionless surface with a velocity of ( 10 m s^{-1} ) hits another 2 kg mass kept at rest, in an inelastic collision. After collision, if they move together, A. they travel with a velocity of ( 5 m s^{-1} ) in the same direction B. they travel with a velocity of ( 10 mathrm{ms}^{-1} ) in the same direction c. they travel with a velocity of ( 10 m s^{-1} ) in the opposite direction D. they travel with a velocity of ( 5 m s^{-1} ) in the opposite direction | 11 |

828 | Find the angle that the vector ( vec{A}=2 hat{i}+ ) ( 3 hat{j}-hat{k} ) makes with y-axis. A ( cdot theta=cos ^{-1}left(frac{3}{sqrt{14}}right) ) B. ( theta=cos ^{-1}left(frac{2}{sqrt{14}}right) ) ( ^{mathrm{c}} cdot_{theta}=cos ^{-1}left(frac{3}{sqrt{16}}right) ) D. ( theta=cos ^{-1}left(frac{3}{sqrt{28}}right) ) | 11 |

829 | A bullet of mass ( m ) moving horizontally with a velocity ( v ) strikes a block of wood of mass ( M ) and gets embedded in the block. The block is suspended from the ceiling by a massless string. The height to which block rises is: ( A ) [ frac{v^{2}}{2 g}left(frac{m}{M+m}right)^{2} ] в. [ frac{v^{2}}{2 g}left(frac{M+m}{m}right)^{2} ] ( ^{mathrm{c} cdot} frac{v^{2}}{2 g}left(frac{m}{M}right)^{2} ) ( D ) [ frac{v^{2}}{2 g}left(frac{M}{m}right)^{2} ] | 11 |

830 | 29. Work done by the boy is – mgh 6. mgh mgh mgh d. None of above | 11 |

831 | A metallic ball strikes a wall and falls down whereas a tennis bail having the same mass and velocity bounces back. The reason for this is that: A. both suffer equal change in momentum. B. the tennis ball suffers a greater change in momentum c. metallic ball suffers a greater change in momentum. D. the momentum of the tennis ball is less than that of the metallic ball | 11 |

832 | 9. A block of mass m is dropped onto a spring of constant k from a height h. The second end of the spring is attached to a second block of mass M as shown in Fig. 8.213. Find the minimum value of h so that the block M bounces off the ground. if the block of mass m sticks to the spring immediately after it comes into contact with it. Fig. 8.213 mottoehad with a macelana | 11 |

833 | Kinetic energy of a body depends upon its: A. mass B. velocity c. density D. both A and | 11 |

834 | Illustration 8.5 A force F = a + bx acts on a particle in X-direction, where a and b are constants. Find the work done by this force during the displacement from x, to X2. | 11 |

835 | A box of weight ( 150 k g f ) has ( 1.47 k J ) of gravitational potential energy stored in it. Find the height of the box above the ground. Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{N} boldsymbol{k} boldsymbol{g}^{-1} ) A . ( 10 m ) в. 4.9 т c. ( 2.45 m ) D. ( 1 m ) | 11 |

836 | If ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{boldsymbol{i}}+hat{boldsymbol{j}}-hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=sqrt{mathbf{2}}(hat{boldsymbol{i}}+hat{boldsymbol{j}}) ) Find ( vec{A} . vec{B} ). Hence find the angle between ( vec{A} ) and ( vec{B} ). Also find the component of ( overrightarrow{boldsymbol{A}} ) along ( overrightarrow{boldsymbol{B}} ) | 11 |

837 | The force exerted by a compression device is given by ( F(x)=k x(x-l) ) for ( 0 leq x leq l, ) where ( l ) is the maximum possible compression, ( x ) is the compression and ( k ) is the constant Work done to compress the device by a distance ( d ) will be maximum when A ( cdot d=frac{l}{4} ) в. ( d=frac{l}{sqrt{2}} ) ( c cdot d=frac{l}{2} ) D. ( d=l ) | 11 |

838 | – Vi Quvve 8. Which of the following statements is correct? a. Kinetic energy of a system can be changed without changing its momentum. b. Kinetic energy of a system cannot be changed without changing its momentum. c. Momentum of a system cannot be change | 11 |

839 | When two bodies stick together after collision, the collision is said to be: A. partially elastic B. elastic c. inelastic D. perfectly inelastic | 11 |

840 | (a), (V) dll ) 7. In an ideal pulley particle system, mass m, is connected with a vertical spring of stiffness k. If mass m, is released from rest, when the spring is undeformed, find the maximum compression of the reelle Fig. 8.211 | 11 |

841 | A simple pendulum is released from ( boldsymbol{A} ) as shown in figure. If ( m ) and ( l ) represent the mass of the bob and the length of the pendulum respectively, the gain in kinetic energy at ( B ) is then A ( cdot frac{m g}{2} ) B. ( frac{m g}{sqrt{2}} ) ( c ) D. ( frac{2}{sqrt{3}} m g l ) | 11 |

842 | A block is constrained to move along ( x ) axis under a force ( F=-2 x ). Here, ( F ) is in newton and ( x ) in metre. Find the work done by this force when the block is displaced from ( x=2 m ) to ( x=-4 ) m. A . -4 J B. -8J c. -12 D. -16 | 11 |

843 | toppr Q Type your question velocity of the chain suddenly and without frictional resistance or interference from the support or from adjacent links Choose the incorrect statement (when ( x=0, text { then } v=0) ) (length of the chain is L and p is the mass per unit length of the chain) A ( cdot ) the velocity v of the chain as a function of ( x ) is ( sqrt{frac{2 g x}{3}} ) B. the acceferation of a of the falling chain as a function fris ( frac{g}{3} ) C. the energy Q lost from the system as the last link leaves the plafform is ( frac{p g L^{2}}{6} ) D. tension at the middle point of falling chain is ( frac{p g x}{3} ) | 11 |

844 | Tllustration 8.22 A block of mass m is moving with an initial velocity vo towards a stationary spring of stiffness k attached to the wall as shown in Fig. 8.51. m 000004 Fig. 8.51 a. Find the maximum compression in the spring. b. Is the work done by the spring negative or positive? | 11 |

845 | A body is projected at an angle of ( 60^{circ} ) with the horizontal. If its kinetic energy at maximum height is ( 10 mathrm{J} ), then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is : A. half of the maximum height B. two third of the maximum height c. one sixth of the maximum height D. insufficient data to solve the problem. | 11 |

846 | During any collision A. Momentum is conserved B. Linetic energy is conserved c. Both conserved D. All | 11 |

847 | A body of mass ( 6 k g ) is under a force of ( 6 N ) which causes displacement in it given by ( S=frac{t^{2}}{4} m ) where ‘t’ is time. The work done by the force in ( 2 s ) is : A . ( 12 . J ) в. ( 9 J ) ( c .6 J ) D. ( 3 J ) | 11 |

848 | Which of the following is approximately the rate of solar energy (in ( mathbf{K W}) ) falling per ( mathbf{m}^{2} ) on the surface area of the earth? A . в. 100 c. ( 0 . ) D. 0.0001 | 11 |

849 | In a gravity free space, a man of mass ( M ) standing at a height ( h ) above the floor throws a stone of mass ( boldsymbol{m} ) downwards with a speed ( u . ) When the stone reaches the floor, distance of the man above the floor will be : ( A cdot h ) B. ( 2 h ) c. ( _{h}-frac{2 m h}{M} ) D. ( frac{m h}{M}+h ) | 11 |

850 | A plot of velocity versus time is shown in figure. A single force acts on the body The correct statement is A. In moving from ( c ) to ( D ), work done by the force on the body is positive B. In moving from B to C, work done by the force on the body is positive c. In moving from A to B, the body does negative work D. In moving from o to A, work is done by the body and negative | 11 |

851 | Two blocks ( A ) and ( B ) of masses ( m ) and ( 2 mathrm{m} ) respectively placed on a smooth floor are connected by a spring. A third body ( C ) of mass ( m ) moves with velocity ( boldsymbol{v}_{0} ) along the line joining ( mathbf{A} ) and ( mathbf{B} ) and collides elastically with A. At a certain instant of time after collision it is found that the instantaneous velocities of ( A ) and ( mathrm{B} ) are same then : A. the common velocity of A and B at time to is ( v / 3 ). в. [ text { the spring constant is } mathrm{k}=frac{3 m v_{0}^{2}}{2 x_{0}^{2}} ] ( c ) [ text { the spring constant is } mathrm{k}=frac{2 m v_{0}^{2}}{3 x_{0}^{2}} ] D. none of these | 11 |

852 | The total work done on a particle is equal to the change in its kinetic energy. This statement is true for which of the condition? A. always B. only if the forces acting on the body are conservative C. only if the forces acting on the body are gravitational D. only if the forces acting on the body are elastic. | 11 |

853 | A man moves on a straight horizontal road with a block of mass ( 2 k g ) in his hand. If he covers a distance of ( 40 m ) with an acceleration of ( 0.5 m / s^{2}, ) find the work done by the man on the block during the motion. | 11 |

854 | A ball which is at rest is dropped from height ( h ) metre. As it bounces off the floor, its speed is ( 80 % ) of what it was just before touching the ground. The ball will then rise to nearly a height. ( mathbf{A} cdot 0.94 h ) B. ( 0.74 h ) c. ( 0.64 h ) D. ( 0.84 h ) | 11 |

855 | Illustration 8.6 The displacement of a particle of mass 3 on a horizontal smooth surface is a function of time given by x==1 Find out the work done by the external agent for the first one second. | 11 |

856 | 42. Two ends A and B of a smooth chain of mass m and length I are situated as shown in Fig. 8.236. If an external agent pulls A till it comes to same level of B, work done by external agent is sloveeelllllllll somboooo 0000000000000000000 Fig. 8.2360 mgl 36 b. mgl 15 mgl d. None of the above | 11 |

857 | A mass of ( 1 k g ) is thrown up with velocity of ( 1000 m / s . ) After 5 second, it explodes into two parts. One part of mass 400 g moves soen with a velocity ( 25 m / s ) calculate the velocity of other part just after the explosion ( left(boldsymbol{g}=mathbf{1 0 m s}^{-mathbf{2}}right) ) | 11 |

858 | S. A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed V, the electrical power output will be proportional to (IIT JEE, 2000) b. v2 c. p d. A | 11 |

859 | An object of mass ( mathrm{m} ) is tied to a string of length I and a variable force ( mathrm{F} ) is applied on it which brings the string gradually at angle ( theta ) with the vertical Find the work done by the force ( F ) | 11 |

860 | An object is displaced from point ( mathrm{A}(2 mathrm{m} ) ( 3 m, 4 m) ) to a point ( B(1 m, 2 m, 3 m) ) under a constant force ( overrightarrow{boldsymbol{F}}= ) ( (2 hat{i}+3 hat{j}+4 hat{k}) N . ) Find the work done by this force in this process. A. ( -9 J ) ( J ) B. ( 9 J ) c. ( -18 J ) D. ( 18 J ) | 11 |

861 | A catapult throws a stone of mass 0.10 kg with a velocity of ( 30 mathrm{m} / mathrm{s} ). If ( 25 % ) of the PE of the elastic band is wasted during transmission, find the magnitude of PE. | 11 |

862 | The work done in shifting a particle of mass ( m ) from the centre of earth to the surface of the earth is A. ( -m g R ) B. ( frac{1}{2} m g R ) c. zero D. ( m g R ) | 11 |

863 | A rubber ball drops from a height h and after rebounding twice from the ground, it rises to h/2. The co – efficient of restitution is A ( cdot frac{1}{2} ) в. ( quadleft(frac{1}{2}right)^{frac{1}{2}} ) c. ( quadleft(frac{1}{2}right)^{frac{1}{4}} ) D. | 11 |

864 | A ball of mass ( m ) moving at a speed ( v ) collides with another ball of mass ( 3 mathrm{m} ) at rest. The lighter block comes to rest after collision. The coefficient of restitution is- A ( cdot frac{1}{2} ) B. ( frac{2}{3} ) ( c cdot frac{1}{4} ) D. None of these. | 11 |

865 | Illustration 8.4 A force F = 6xî +2yj displaces a body from 7 = 3ỉ +8j to iz = 5 – 4. Find the work done by the force. OL W | 11 |

866 | A stone of mass ( 10 mathrm{kg} ) is lying at the bed of a lake 5 m deep. If the relative density of the stone is ( 2, ) the amount of work done to bring it to the top of the lake will be ( mathbf{A} cdot 250 J ) B. ( 258 J ) c. ( 345 J ) D. ( 385 J ) | 11 |

867 | The kinetic energy of the body after the collision is A ( cdot frac{11 m v^{2}}{54} ) B. ( frac{m v^{2}}{108} ) c. ( frac{17 m v^{2}}{54} ) D. ( frac{17 m v^{2}}{108} ) | 11 |

868 | A sphere ‘P’ of mass ‘m’ moving with velocity ‘u’ collides head-on with another sphere ‘Q’ of mass ‘m’ which is at rest. The ratio of final velocity of ‘Q’ to initial velocity of ‘P’ is ( . cdot(e= ) coefficient of restitution) A ( cdot frac{e-1}{2} ) ( ^{mathrm{B}}left[frac{e+1}{2}right]^{1 / 2} ) c. ( frac{e+1}{2} ) ( ^{mathrm{D} cdot}left[frac{e+1}{2}right]^{2} ) | 11 |

869 | An example of inelastic collision is: A. scattering of ( alpha ) particle from a nucleus B. collision of ideal gas molecules C. collision of two steel balls lying on a frictionless table D. collision of a bullet with a wooden block | 11 |

870 | 88. Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kgm . The work done in lifting water to the ground from the surface of water in the well 20 m below is (g = 10 ms?) a. 1.4 x 104J b. 1.5 x 104 J c. 9.8 x 10 x 6J d. 18 J | 11 |

871 | When a person stands on a weighing balance, working on the principle of Hooke’s law, it shows a reading of ( 60 mathrm{kg} ) after a long time and the spring gets compressed by ( 2.5 mathrm{cm} . ) If the person jumps on the balance from a height of ( mathbf{1 0} c boldsymbol{m}, ) the maximum reading of the balance will be A. ( 60 mathrm{kg} ) в. ( 120 mathrm{kg} ) c. ( 180 mathrm{kg} ) D. 240 kg | 11 |

872 | A block mass ‘ ( m^{prime} ) is released from rest at point A. The compression in spring, when the speed of block is maximum is: A ( cdot frac{m g sin theta}{k} ) B. ( frac{2 m g sin theta}{k} ) ( c cdot frac{m g cos theta}{k} ) D. ( frac{m g}{k} ) | 11 |

873 | The water stored in a reservoir possesses: A. Kinetic energy B. Muscular energy c. Potential energy D. Magnetic energy | 11 |

874 | 3. A block of mass m lies on a wedge of mass M. The wedge in turn lies on a smooth horizontal surface. Friction is absent everywhere. The wedge-block system is released from rest. All situations given in Column I are to be estimated in duration the block undergoes a vertical displacement h starting from rest. Match the statements in Column I with the results in Column II. (g is acceleration due to gravity.) Fig. 8.293 Column I Column II i. Work done by normal reaction a. positive acting on the block is ii. Work done by normal reaction b. negative (exerted by block) acting on the wedge is iii. The sum of work done by normal c. zero reaction on the block and work done by normal on wedge iv. Net work done by all forces on d. less than mgh in the block is magnitude | 11 |

875 | A cord is used to raise a block of mass ( m ) vertically through a distance ( d ) at a constant downward acceleration ( boldsymbol{g} / mathbf{4} ) The work done by the cord is: ( mathbf{A} cdot m g d / 4 ) в. ( 3 M g d / 4 ) c. ( -3 M g d / 4 ) D. ( M g d ) | 11 |

876 | Graph shows the acceleration of ( 3 g ) particle as an applied force moves it from rest along ( boldsymbol{x} ) – axis. The total work done by the force on the particle by the time the particle reaches ( boldsymbol{x}=mathbf{6 m}, ) is equal to | 11 |

877 | A body of mass 10 gm moving with a velocity of ( 20 mathrm{cm} s^{-1} ) collides with a stationary mass of ( 90 mathrm{gm} ). The collision is perfectly inelastic. Find the percentage loss of kinetic energy of the system. A. B. 50 c. 90 D. 100 | 11 |

878 | One joule is approximately equal to: A. 0.28 call ( l ) в. 0.32 сад ( l ) c. 0.24 call ( l ) D. 4.2 call ( l ) | 11 |

879 | A body is projected vertically up from a point on the ground. When it is at a height ( h ) above the ground, its kinetic and potential energies are found to be in the ratio of ( 3: 2 . ) If the body rises to a maximum height of ( H ) above the ground, then the ratio of ( boldsymbol{H}: boldsymbol{h} ) will be A . 5: 3 B . 2: 1 c. 5: 2 D. 2: 5 | 11 |

880 | Which of the following physical quantity is different from others? A. Displacement B. Velocity c. Force D. Kinetic energy | 11 |

881 | The angle made by ( overrightarrow{mathrm{j}}+overrightarrow{mathrm{k}} ) with ( mathrm{y} ) -axis is: A ( cdot 60^{circ} ) B. ( 30^{circ} ) ( mathbf{c} cdot 45^{circ} ) D. ( 90^{circ} ) | 11 |

882 | Two solid rubber balls, A and B having masses 200 and 400 g respectively are moving in opposite directions with velocity of A equal to ( 0.3 m / s ). After collision the two balls come to rest, then the velocity of B is- A. ( 0.15 mathrm{m} / mathrm{s} ) в. ( 1.5 mathrm{m} / mathrm{s} ) c. ( -0.15 mathrm{m} / mathrm{s} ) D. None of the above | 11 |

883 | A body of mass 2 kg starts with an initial velocity ( 5 mathrm{m} / mathrm{s} ). If the body is acted upon by a time dependent force (F) as shown in figure, then work done on the body in 20 s is? | 11 |

884 | A body of mass ( 3 k g ) is under a constant force which causes a displacement s in metres in it given by the relation ( s= ) ( frac{1}{3} t^{2}, ) where ( t ) is in a workdone by the force in ( 2 s ) is | 11 |

885 | A particle of mass ( boldsymbol{m}=12 boldsymbol{k} boldsymbol{g} ) falling freely from rest under gravity and air resistance force ( (boldsymbol{F}) ). The velocity of the particle when reaches ground is ( 6 m / s ) Then total external work done on the particle is ( mathbf{A} cdot 216 J ) в. ( (120-F) J ) ( mathbf{c} .6 F J ) D. Data insufficient | 11 |

886 | A force ( F ) is applied on a lawn mower at an angle of ( 60^{circ} ) with the horizontal. If it moves through a distance ( x ) in horizontal direction, the work done by the force is: A ( cdot frac{F x}{2} ) в. ( frac{sqrt{3} F x}{2} ) c. ( 2 F x ) D. None of the above | 11 |

887 | ( n ) elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius ( r ) as shown in the figure. The masses of the balls are ( m, frac{m}{2}, frac{m}{2^{2}} ldots ldots frac{m}{2^{n-1}} ) respectively. What is the minimum velocity which should be imparted to the first ball of mass ( m ) such that ( n^{t h} ) ball completes the vertical circle: A ( cdotleft(frac{3}{4}right)^{n-1} sqrt{5} g r ) В ( cdotleft(frac{4}{3}right)^{n-1} sqrt{5 g r} ) c. ( left(frac{3}{2}right)^{n-1} sqrt{5 g r} ) D ( cdotleft(frac{2}{3}right)^{n-1} sqrt{5 g r} ) | 11 |

888 | Book of mass ( 2 mathrm{kg} ) is lifted from floor to the table. The height between floor and the table is ( 1.5 mathrm{m} ). Calculate the work done by gravitational force. A . -30 B . -15 J c. о D. 15 J E. 30 | 11 |

889 | A block of mass ( m ) moving at a speed ( v ) collides with another block of mass ( 2 m ) at rest. The lighter block comes to rest after collision. What is the coefficient of restitution. | 11 |

890 | A cart ( A ) of mass ( 50 k g ) moving at a speed of ( 20 k m / h ) hits a lighter cart ( B ) of mass ( 20 mathrm{kg} ) moving towards it at a speed of ( 10 mathrm{km} / mathrm{h} ). The two carts cling to each other. Find the change of momentum of cart A. | 11 |

891 | A wound watch spring has energy. A. mechanical B. kinetic C . potential D. kinetic and potential | 11 |

892 | Illustration 8.31 8.31 A 4.00-kg particle moves from the origin A 4.00-kg particle moves to position C, having coordinate x = 5.00 m and y on the particle is the gravitational force acting in the negative y direction. Using equation W=Far ork done by the gravitational force on the particle as it goes from O to Calong (a) OAT, (D) (C) OC. Your results should all be identical. Why? sequation W=FArcos O=F. AF. (5.00,5.00)m Fig. 8.68 | 11 |

893 | A force of ( 10 mathrm{N} ) is applied on an object at rest of mass ( 2 mathrm{kg} ) placed on a smooth surface. The kinetic energy after 5 s is ( J ) A . 124.6 в. 625 c. 312.5 D. 683.8 | 11 |

894 | A bullet is fired at a target with a velocity ( 80 mathrm{m} / mathrm{s} ) and penetrates ( 50 mathrm{cm} ) into it. If this bullet were fired into a target ( 25 mathrm{cm} ) thick with equal velocity, with what velocity would it emerge, supposing the resistance to be uniform and the same in both the cases? A. ( sqrt{80} mathrm{m} / mathrm{s} ) в. ( frac{40}{sqrt{2}} m / s ) c. ( 40 m / s ) D. ( 40 sqrt{2} mathrm{m} / mathrm{s} ) | 11 |

895 | A particle of mass M moves along the ( x ) axis with speed ( V_{0} ) and collides and sticks to a particle of mass ( m ) moving with a speed ( V_{0} ) along y-axis. The velocity of the combined particle after the collision: ( ^{mathbf{A}} cdot frac{M hat{i}+m hat{j}}{(M+m)} V_{0} ) B. ( frac{m hat{i}+M hat{j}}{(M+m)} V_{0} ) c. ( (m hat{i}+M hat{j}) V_{0} ) D. Zero | 11 |

896 | Angle (in rad) made by the vector ( sqrt{3} hat{i}+hat{j} ) with the ( x ) -axis: A ( cdot frac{pi}{6} ) B. ( c cdot frac{pi}{3} ) D. | 11 |

897 | A particle of mass ( m ) is located in a one dimensional potential field where potential energy is given by ( U(x)=A(1- ) ( cos p x), ) where ( A ) and ( p ) are constants. The period of small oscillations of the particle A ( cdot 2 pi sqrt{frac{m}{A p^{2}}} ) в. ( pi sqrt{frac{m}{A P}} ) c. ( pi sqrt{frac{m}{A}} ) D. ( left(frac{1}{2 pi}right) sqrt{frac{A p}{m}} ) | 11 |

898 | A body of mass ( m ) is lifted up from the surface of earth to a height three times the radius of the earth ( R ) The change in potential energy of the body is A. ( 3 m g R ) в. ( frac{5}{4} ) mg ( R ) c. ( frac{3}{4} m g R ) D. ( 2 m g R ) | 11 |

899 | The car ( A ) of mass ( 1500 k g ) travelling at ( 40 m / s ) collides with another car ( ^{prime} B^{prime} ) of mass ( 1250 k g ) travelling at ( 25 m / s ) in the same direction. After collision the velocity of car ‘ ( A^{prime} ) becomes ( 30 m / s ) calculate the velocity of car ( ^{prime} B^{prime} ) after the collision. | 11 |

900 | A cricket ball of mass ( mathrm{m} ) is hitted at the angle ( 45^{circ} ) to the horizontal with velocity v.lts kinetic energy at the topmost point is ( mathbf{A} cdot mathbf{0} ) B ( cdot frac{1}{2} m v^{2} ) c. ( frac{m v^{2}}{4} ) D. ( frac{m v^{2}}{2 sqrt{2}} ) | 11 |

901 | A vertical narrow smooth tube is bent from it’s diameter such that one semicircular part of the tube is horizontal and the other part is vertical A smooth ball is released from the highest point of the tube. If the maximum speed of ball is ( boldsymbol{x} boldsymbol{m} / boldsymbol{s}, ) then the value of ( x ) is : (neglect collision at bending) (take ( boldsymbol{R}=mathbf{2 . 5 m} ) and ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} ) | 11 |

902 | A truck and a car are moving on a smooth, level road such that the K.E. associated with them is the same. Brakes are applied to both of them simultaneously. Which one will cover a greater distance before it stops? A . car B. truck c. the same distance D. nothing can be decided | 11 |

903 | Two identical balls of equal masses ( A ) and ( mathrm{B} ), are lying on a smooth surface as shown in the figure. Ball A hits the ball B (which is at rest) with a velocity ( v= ) ( 16 m s^{-1} . ) What should be the minimum value of coefficient of restitution between ( A ) and ( B ) so that ( B ) just reaches the highest point of inclined plane? ( left(g=10 m s^{-2}right) ) A ( cdot frac{2}{3} ) B. ( frac{1}{4} ) ( c cdot frac{1}{2} ) D. ( frac{1}{3} ) | 11 |

904 | What is the nature of force between the colliding bodies? A. External B. conservative ( c . ) Internal D. Non conservative | 11 |

905 | If ( g ) is acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( m ) raised from the surface of earth to a height equal to the radius ( R ) of the earth is ( ^{mathbf{A}} cdot frac{1}{2}^{m g R} ) в. ( 2 m g R ) ( mathrm{c} cdot m g R ) D. ( frac{1}{4} m g R ) | 11 |

906 | 22. The potential energy curve for interaction between two molecules is shown in Fig. 8.277. Which of the following statements are true? a. The molecules have maximum attraction for r=0A. OHAB co Fig. 8.277 b. The molecules have maximum kinetic energy for r = OB. c. The intermolecular force is zero for r = OB. d. For the gaseous state, the depth BD of the potential energy curve is much smaller than KT. | 11 |

907 | 78. A moving railway compartment has a spring of constant k fixed to its front wall. A boy stretches this spring by distance x and in the mean time the compartment moves by a distance s. The work done by boy w.r.t. earth is ロロロロロロ AUW Fig. 8.256 – kx² b. (kx) (s + x) kxs kx(stxts) 1 111 | 11 |

908 | A body is dropped from a certain height. When it loses ( U ) amount of its energy it acquires a velocity’ ( v^{prime} . ) The mass of the body is: A ( cdot 2 U / v^{2} ) B ( cdot 2 v / U^{2} ) c. ( 2 v / U ) D. ( U^{2} / 2 v ) | 11 |

909 | Derive an expression for work done in sliding body down a rough inclined plane | 11 |

910 | A uniform bar of mass ( M ) and length ( L ) collides with a horizontal surface. Before collision, velocity of centre of mass was ( v_{0} ) and no angular velocity. Just after collision, velocity of centre of mass of bar becomes ( boldsymbol{v} ) in upward direction as shown. Angular velocity ( omega ) of the bar just after impact is: ( A ) в. c. ( frac{left(v_{0}+vright) cos theta}{L} ) ( D ) | 11 |

911 | 53. One end of an unstretched vertical spring is attached to the ceiling and an object attached to the other end is slowly lowered to its equilibrium position. If S is the gain in spring energy and G is the loss in gravitational potential energy in the process, then a. S=G b. S=2G c. G= 2S d. None of these | 11 |

912 | The maximum vertical distance through which a fully dressed astronaut canjump on the earth is ( 0.5 m . ) If mean density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical distance which he can jump on the Moon and the ratio of the time of duration of the jump on the Moon to hold on the earth are в. ( 6 m, 3: ) ? ( c .3 m, 1: 6 ) D. ( 6 m, 1: 6 ) | 11 |

913 | A ball moving with velocity ( 2 m / s ) collides head on with another stationary ball of double the mass. If the coefficient of restitution is ( 0 cdot 5, ) then their velocities ( (operatorname{in} m / s) ) after collision will be A . 0,1 в. 1,1 c. ( 1,0 cdot 5 ) D. 0,2 | 11 |

914 | A ball of mass m moving with velocity collides elastically with another ball of identical mass coming from the opposite direction with velocity ( 2 v ) Their velocities after collision are : A . ( -v, 2 v ) в. ( -2 v, v ) c. ( v,-2 v ) D. ( 2 v,-v ) | 11 |

915 | A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is A ( cdot frac{11}{12} ) B. ( frac{2}{11} ) c. ( frac{48}{121} ) D. ( frac{48}{169} ) | 11 |

916 | ( underbrace{[L atop L} ) | 11 |

917 | A body is moved in a direction opposite to the direction of force acting on it. Work is done is: A. against the force B. zero c. along the force D. none of these | 11 |

918 | Potential energy of an object raised through a height h is ( (1 / 2 ) ( left.m v^{2}, m g hright) ) | 11 |

919 | Identify the correct statement about work energy theorem This question has multiple correct options A. work done by all the conservative forces is equal to the decrease in potential energy. B. work done by all the forces except the conservative forces is equal to the change in mechanical energy. C. work done by all the forces is equal to the change in kinetic energy. D. work done by all the forces is equal to the change in potential energy. | 11 |

920 | Two vectors ( A ) and ( sqrt{3} A ) are acting perpendicular to each other. What is the angle of resultant vector with ( boldsymbol{A} ) | 11 |

921 | A particle of mass ( m ) is moving along ( x- ) axis with speed ( v ) when it collides with a particle of mass ( 2 m ) initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two places? ( (boldsymbol{theta}>mathbf{0}) ) A. each piece moves with speed ( v ). B. each piece moves with speed ( v / 2 ) c. one of the piece moves with speed ( v / 2 ), the other moves with speed greater than ( v / 2 ). D. each piece moves with speed greater than ( v / 2 ) | 11 |

922 | Q Type your question weighs ( m^{prime} . ) Ejection of fuel gas is at a constant rate of ( m_{0} ) per second with a constant velocity of ( u_{r e l} ) relative to the rocket. Final speed of rocket after the complete burn out of the fuel is given by ( boldsymbol{v}= ) ( ^{mathbf{A}} cdot_{u_{r e l}} log _{e} frac{m}{m^{prime}} ) в. ( quad u_{r e l} log _{e} frac{m_{0}}{m} ) ( ^{mathrm{c}} cdot_{-u_{r e l}} log _{e} frac{m_{0}}{m^{prime}} ) D. ( -u_{r e l} frac{d m}{m} ) | 11 |

923 | elevated ends and a flat central part as shown in the Figure below. The flat portion BC has a length ( l=3.0 m . ) The curved portions of the track are frictionless. For the flat part the coefficient of kinetic friction is ( mu_{k}= ) ( 0.20, ) the particle is released at point ( A ) which is at height ( h=1.5 m ) above the flat part of the track. Where does the particle finally comes to rest? B. The particle comes to rest at ( frac{1}{4} ) th distance from the point B of the flat part. C. The particle comes to rest at ( frac{3}{4} ) th distance from the point B of the flat part. D. The particle comes to rest at point | 11 |

924 | Two identical smooth balls are projected from points 0 and ( A ) on the horizontal ground with same speed of projection. the angle of projection in each case is ( 30^{circ} ) (see figure). The distance between 0 and ( A ) is 100 m. The balls collide in mid-air and return to their respective points of projection. If the coefficient of restitution is ( 0.7, ) find the speed of projection of either ball (in ( mathrm{m} / mathrm{s}) ) correct to nearest integer. (Take ( left.g=10 m s^{-2} text {and } sqrt{3}=1.7right) ) | 11 |

925 | A ball strikes a horizontal floor at ( 45^{circ} .25 % ) of its kinetic energy is lost collision. Find the coefficient of restitution A . в. ( frac{1}{sqrt{2}} ) c. ( frac{1}{sqrt{4}} ) D. | 11 |

926 | A man applying a force ( boldsymbol{F} ) upon a stretched spring is stationary in a compartment moving with constant speed ( v . ) If the compartment covers a distance ( L ) in some time ( t, ) then This question has multiple correct options A. The man acting with force F on spring does the work ( (w)=F L ) B. The total work performed by man on the compartment with respect to ground is zero c. The work done by friction acting on man with respect to ground is, (w) ( =F L ) D. The total work done by man with respect to ground is ( (w)=F L ) | 11 |

927 | A ball of mass ( 10 mathrm{kg} ) is moving with a velocity of ( 10 mathrm{m} / mathrm{s} ). It strikes another ball of mass ( 5 mathrm{kg} ), which is moving in the same direction with a velocity of ( 4 mathrm{m} / mathrm{s} ) If the collision is elastic their velocities after collision will be respectively: A ( cdot 12 mathrm{m} / mathrm{s}, 6 mathrm{m} / mathrm{s} ) B. ( 12 mathrm{m} / mathrm{s}, 25 mathrm{m} / mathrm{s} ) ( c cdot 6 m / s, 12 m / s ) D. ( 8 mathrm{m} / mathrm{s}, 20 mathrm{m} / mathrm{s} ) | 11 |

928 | A bullet of mass m moving with a velocity ( v_{1} ) strikes a suspended wooden block of mass ( mathrm{M} ) as shown in the figure and sticks to it. If the block rises to a height h the initial velocity of the bullet is- A ( cdot frac{m+M}{m} sqrt{2 g h} ) ( mathbf{B} cdot sqrt{2 g h} ) c. ( frac{M+m}{m} sqrt{g h} ) D. ( frac{m}{M+m} sqrt{2 g h} ) | 11 |

929 | A body is displaced from (0,0) to ( (1 m, 1 m) ) along the path ( x=y ) by a force ( boldsymbol{F}=left(boldsymbol{x}^{2} hat{boldsymbol{j}}+boldsymbol{y} hat{boldsymbol{i}}right) boldsymbol{N} . ) The work done by this force will be : A ( cdot frac{4}{3} J ) в. ( frac{5}{6} J ) ( c cdot frac{3}{2} J ) D. ( frac{7}{5} J ) | 11 |

930 | A mass ( m ) is placed at point ( P ) lies on the axis of a ring of mass ( mathrm{M} ) and radius ( R ) at a distance ( R ) from its centre. The gravitational force on mass ( mathrm{m} ) is then ( ^{mathbf{A}} cdot frac{G M m}{sqrt{2} R^{2}} ) в. ( frac{G M m}{2 R^{2}} ) c. ( frac{G M m}{2 sqrt{2} R^{2}} ) D. ( frac{G M m}{4 R^{2}} ) | 11 |

931 | A ball is dropped on to a horizontal plate from a height ( h=9 mathrm{m} ) above it. If the coefficient of restitution is ( e=1 / 2, ) the total distance travelled before the ball comes to rest is A . ( 10 mathrm{m} ) B. 15 ( m ) ( c cdot 20 m ) D. 25 m | 11 |

932 | A parallel beam of particles of mass ( m ) moving with velocities ( v ) impinges on a wall at an angle ( theta ) to its normal. The number of particles per unit volume in the beam is ( n ). if the collision of particles with the wall is elastic, then find the pressure exerted by this beam on the wall. | 11 |

933 | What do you understand by work? | 11 |

934 | A light rigid rod of length ( boldsymbol{L}=frac{8}{5} mathrm{m} ) hinged at one end has a bob of mass ( mathrm{m} ) attached to its other end. Find speed (in ( mathrm{m} / mathrm{s} ) ) of bob at the lowest point when rod is released from vertical position. | 11 |

935 | ( mathbf{A} ) 1 kg stationary bomb is exploded in three parts having mass ratio 1: 1: 3 Parts having same mass move in perpendicular directions with velocity ( 30 m / s, ) then the velocity of bigger part will be: ( mathbf{A} cdot 10 sqrt{2} mathrm{m} / mathrm{s} ) В. ( frac{10}{sqrt{2}} m / s ) c. ( 15 sqrt{2} mathrm{m} / mathrm{s} ) D. ( frac{15}{sqrt{2}} m / s ) | 11 |

936 | Two bodies of masses ( 0.1 k g ) and ( 0.4 k g ) move towards each other with velocities ( 1 m / s ) and ( 0.1 m / s ) respectively. After collision they stick together. In ( 10 s ) the combined mass travels ( mathbf{A} cdot 120 m ) B. ( 0.12 m ) ( c .12 m ) D. ( 1.2 m ) | 11 |

937 | Which of the following is not an example of potential energy? A. A vibrating pendulum at its maximum displacement from the mean position B. A body at rest at some height from the ground C. A wound clock-spring D. A vibrating pendulum when it is just passing through the mean position | 11 |

938 | A bullet of mass ( 20 g ) is moving with a speed of ( 150 mathrm{ms}^{-1} . ) It strikes a target and is brought to rest after piercing 10 ( c m ) into it. Calculate the average force of resistance offered by the target. A ( .2500 mathrm{N} ) в. 2000 J c. ( 2250 N ) D. 2100 J | 11 |

939 | Light with an energy flux of ( 20 mathrm{W} / mathrm{cm}^{2} ) falls on a non-reflecting surface at normal incidence. If the surface has an area of ( 30 mathrm{cm}^{2} ), the total momentum delivered (for complete absorption) during 30 minutes is : A ( .3 .6 times 10^{-3} mathrm{kg} mathrm{m} / mathrm{s} ) B. ( 3.3 times 10^{-8} mathrm{kg} mathrm{m} / mathrm{s} ) c. ( 10.8 times 10^{4} mathrm{kg} mathrm{m} / mathrm{s} ) D. ( 1.08 times 10^{7} mathrm{kg} mathrm{m} / mathrm{s} ) | 11 |

940 | A body of mass ‘ ( m ) ‘ is raised to a height ( 10 R^{prime} ) from the surface of the Earth, where ‘ ( R^{prime} ) is the radius of the Earth. The increase in potential energy is ( G= ) universal constant of gravitation, ( M= ) mass of earth and ( g= ) acceleration due to gravity) ( ^{A} cdot frac{G M m}{11 R} ) в. ( frac{G M m}{10 R} ) c. ( frac{m g R}{11 G} ) D. ( frac{10 G M m}{11 R} ) | 11 |

941 | A car is going with a linear momentum p. When brakes are applied, it comes to a stop in a distance ( s ). If the same car were going with a linear momentum ( 2 p ) and the brakes are applied, it comes to a stop in a distance of (assume that the brake force is same in the two cases) ( mathbf{A} cdot 2 s ) B. c. ( 4 s ) D. | 11 |

942 | A bomb of mass 9 kg explodes into two pieces of masses ( 3 mathrm{kg} ) and 6 kg. The velocity of mass ( 3 mathrm{kg} ) is ( 16 mathrm{ms}^{-1} ). The kinetic energy of mass ( 6 mathrm{kg} ) is A . 96 J B. 384 J c. 192 J D. 768 J | 11 |

943 | A particle moves in such a way that its position vector at any time ( t ) is ( vec{r}=t hat{i}+ ) ( frac{1}{2} t^{2} hat{j}+t hat{k} . ) Find as a function of time (i) the velocity ( left(frac{d vec{r}}{d t}right) ) (ii) the speed ( left(left|frac{d vec{r}}{d t}right|right) ) (iii) the acceleration ( left(frac{boldsymbol{d} overrightarrow{boldsymbol{v}}}{boldsymbol{d} boldsymbol{t}}right) ) (iv) the magnitude of the acceleration (v) the magnitude of the component of acceleration along velocity (called tangential acceleration) (vi) the magnitude of the component of acceleration perpendicular to velocity (called normal acceleration). | 11 |

944 | A pair of starts rotates about a common centre of mass. One of the stars has a mass ( M ) and the other ( m ). Their centres are a distance ( d ) apart, ( d ) being large compared to the size of either star. Derive an expression for the period of revolution of the stars about their common centre of mass. Compare their angular momenta and kinetic energies. | 11 |

945 | A block of mass ( 2.0 mathrm{kg} ) is pushed down an inclined plane of inclination ( 37^{circ} ) with a force of ( 20 N ) acting parallel to the incline. It is found that the block moves on the incline with an acceleration of ( 10 m / s^{2} . ) If the block started from rest, find the work done (a) by the applied force in the first second A . 100 B. 105 c. 150 D. 200 | 11 |

946 | Block A has a weight of 300N and block B has a weight of 50 N. If the coefficient of kinetic friction between the incline and block ( A ) is ( mu_{k}=0.2 . ) Determine the speed of block A after it moves ( 1 mathrm{m} ) down the plane, starting from rest. Neglect the mass of the cord and pulleys. | 11 |

947 | The energy required to raise a given volume of water from a well can be A. Mega watts B. Mega newton c. Mega joules D. Kilo watts | 11 |

948 | If a body of mass ( 200 g ) falls from a height ( 200 m ) and its total potential energy is conserved into kinetic energy, at the point of contact of the body with the surface, then decrease in potential energy of the body at the contact is begin{tabular}{l} A. 9005 \ hline end{tabular} в. ( 500 J ) c. ( 400 J ) D. ( 200 J ) | 11 |

949 | If a simple pendulum of mass ( boldsymbol{m} ) is displaced by a distance of ( x ) from its mean position, then find the potential energy stored in it. | 11 |

950 | A body when acted upon by a force of 10 ( k g f ), gets displaced by ( 0.5 m ) normal to the force. Calculate the work done by the force, when the displacement is in the direction of force. A . ( 5 . J ) в. ( 500 J ) c. ( 0.5 J ) D. ( 50 J ) | 11 |

951 | i ule paul in between tol surface. A 4. A long block A is at rest on a smooth horizontal surface. A small block B whose mass is half of mass of A is placed on A at one end and is given an initial velocity u as shown in Fig. 8.274. The coefficient of friction between the blocks is u. HB Smooth Fig. 8.274 a. Finally both move with a common velocity 2u/3. b. Acceleration of B relative to A initially is 3ug/2 towards left. c. Magnitude of total work done by friction is equal to the final kinetic energy of the system. d. The ratio of initial to final momentum of the system is 1. Choose the correct statement(s) from the following | 11 |

952 | A block ( A, ) whose weight is ( 200 N ), is pulled up a slope of length ( 5 m ) by means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) ) as illustrated in Figure. What is the work done by the force ( boldsymbol{F} ) in moving the block ( A, 5 m ) along the slope? A ( .450 J ) B. ( 600 J ) ( c .0 J ) D. ( 750 J ) | 11 |

953 | A body of volume ( V ) and density ( rho ) is initially submerged in a liquid of density ( rho^{prime} . ) If it lifted through a height ( h ) in the liquid, its potential energy will: A . increase by ( h Vleft(rho-rho^{prime}right) g ) B. decrease by ( h Vleft(rho-rho^{prime}right) g ) C . increase by ( h V_{rho g / rho} ) D. decrease by ( h V_{rho g / rho} ) | 11 |

954 | Determine the loss in kinetic energy of the system as whole as a result of the collision. ( ^{mathbf{A}} cdot frac{1}{6} m v^{2} ) в. ( frac{1}{7}^{m v^{2}} ) ( mathrm{c} cdot m v^{2} ) D. ( frac{m v^{2}}{5} ) | 11 |

955 | A glass marble dropped from a certain height above the horizontal surface reaches the surface in time ( t ) and then continues to bounce up and down. The time in which the marble finally comes to rest is: ( mathbf{A} cdot e^{n} t ) B . ( e^{2} t ) ( ^{mathbf{c}} cdot tleft[frac{1+e}{1-e}right] ) D. ( tleft[frac{1-e}{1+e}right] ) | 11 |

956 | A ( 0.50 k g ) object moves in a horizontal circular track with a radius of ( 2.5 m . ) An external force of ( 3.0 N, ) always tangent to the track, causes the object to speed up as it goes around. The work done by the external force as the mass makes one revolution is: A ( .24 J ) B. ( 47 J ) c. ( 58 J ) D. ( 67 J ) | 11 |

957 | The negative of the distance rate of change of potential energy is equal to: A. force acting on the particle in the direction of displacement B. acceleration of the particle, perpendicular to displacement c. power D. impulse | 11 |

958 | A block of mass ( 50 mathrm{kg} ) is projected horizontally on a rough horizontal floor. The coefficient of friction between the block and the floor is ( 0.1 . ) The block strikes a light spring of stiffness ( boldsymbol{k}= ) ( 100 N / m ) with a velocity ( 2 m / s . ) The maximum compression of the spring is ( A cdot 1 m ) 3. ( 2 m ) | 11 |

959 | A sphere A impinges directly on an identical sphere ( mathrm{B} ) at rest. If e is the coefficient of restitution then the ratio of the velocities of ( A ) and ( B ) after impact is A ( cdot frac{1+e}{1-e} ) в. ( frac{1-e}{1+e} ) c. ( frac{e}{1-e} ) D. ( frac{e}{1+e} ) | 11 |

960 | Which quantity of a two particles system depend only on the separation between the two particles? A. Kinetic energy B. Total mechanical energy c. Potential energy D. Both (A) and (B) | 11 |

961 | A ball is dropped from a height of ( 1 mathrm{m} ). if coefficient of restitution between the surface and the ball is ( 0.6, ) the ball rebounds to a height of ( A cdot 0.6 m ) B. 0.4 ( m ) ( c cdot 1 m ) D. 0.31 ( m ) | 11 |

962 | Figure shows a wedge ( A ) of mass ( 6 mathrm{m} ) smooth semicircular groove of radius a ( =8.4 mathrm{m} ) placed on a smooth horizontal surface. A small block B of mass m is released from a position in groove where its radius is horizontal. Find the speed (in ( mathrm{ms}^{-1} ) ) of bigger block when smaller block reaches its bottommost position A. ( 3 m / s ) B. ( 2 m / s ) ( c .7 m / s ) ( mathbf{D} cdot 4 m / s ) | 11 |

963 | If a body is taken up to a height of ( 1600 mathrm{km} ) from the earth’s surface, then the percentage loss of gravitational force acting on that body will be – (Radius of earth ( R_{e}=6400 mathrm{km} ) ). A . 50% B. 36% c. 25% D. 10% | 11 |

964 | According to the definition of oblique collision in the paragraph, which of the following collision cannot be oblique? A. Collision between two point masses. B. Collision between two rings of same radius c. collision between two rings of different radius D. All the above | 11 |

965 | A force of ( 5 N ) is applied on a ( 20 k g ) mass at rest. the work done in the third second is:- A ( cdot frac{25}{8} J ) в. ( frac{25}{4} J ) c. ( 12 J ) D. 25J | 11 |

966 | Identify which of the following quantities remain conserved during an elastic collision? A. momentum only B. momentum and potential energy c. kinetic energy only D. momentum and kinetic energy E. momentum end velocity | 11 |

967 | A loud speaker converts: A. electrical energy into sound energy B. sound energy into electrical energy C. mechanical energy into sound energy D. sound energy into mechanical energy | 11 |

968 | rolling on a smooth horizontal surface with velocity ( V ) and angular velocity ( omega ) (where ( V=omega r) . ) The sphere collides with a sharp edge on the wall as shown in the figure. The coefficient of friction between the sphere and the edge ( mu= ) 1/5. Just after the collision the angular velocity of the sphere becomes equal to zero. The linear velocity of the sphere just after the collision is equal to: ( mathbf{A} cdot V ) B. ( underline{V} ) ( overline{5} ) c. ( frac{3 V}{5} ) D. ( frac{V}{6} ) | 11 |

969 | Two satellites ( A ) and ( B ) of the same mass are revolving around the earth in the concentric circular orbits such that the distance of satellite ( B ) from the centre of the earth is thrice as compared to the distance of the satellite ( A ) from the centre of the earth. The ratio of the centripetal force acting on ( B ) as compared to that on ( A ) is A ( cdot frac{1}{3} ) B. 3 c. ( frac{1}{9} ) D. ( frac{1}{sqrt{3}} ) | 11 |

970 | Illustration 3.34 A body constrained to move along the z-axis of a co-ordinate system is subjected to a constant force F given by F=-i +2j+3k newton where i, j, and ſ represent unit vectors along X-, y, and z-axes of the system, respectively. Calculate the work done by this force in displacing the body through a distance of 4 m along the z-axis. | 11 |

971 | A ( 12 k g ) bomb at rest explodes into two pieces of ( 4 k g ) and ( 8 k g . ) If the momentum of ( 4 k g ) piece is ( 20 N s, ) the kinetic energy of the ( 8 k g ) piece is: A ( .25 J ) B. ( 20 J ) c. ( 50 J ) D. ( 40 J ) | 11 |

972 | In one – dimensional head on collision, the relative velocity of approach before collision is equal to: A. relative velocity of separation after collision B. ( e ) times relative velocity of separation after collision c. ( 1 / e ) times relative velocity of separation after collision D. sum of the velocities after collision | 11 |

973 | The velocity of a particle is ( overrightarrow{boldsymbol{v}}=mathbf{6} hat{mathbf{i}}+ ) ( 2 hat{j}-2 hat{k} . ) The component of the velocity parallel to vector ( vec{a}=hat{i}+hat{j}+hat{k} ) is :- ( mathbf{A} cdot 6 hat{i}+2 hat{j}+2 hat{k} ) B . ( 2 hat{i}+2 hat{j}+2 hat{k} ) ( mathbf{c} cdot hat{i}+hat{j}+hat{k} ) D. ( 6 hat{i}+2 hat{j}-2 hat{k} ) | 11 |

974 | A body of mass ( 2 mathrm{kg} ) is thrown vertically upwards with an initial velocity of 20 ( mathrm{m} / mathrm{s} . ) What ( mathrm{m}: ) potential energy at the end of ( 2 s ? g=10 m / s^{2} ) | 11 |

975 | A car is accelerated on a leveled road and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car A. does not change B. becomes twice to that of initial c. becomes 4 times that of initial D. becomes 16 times that of initial | 11 |

976 | Explain by an example that a body may posses energy when it is not in motion. | 11 |

977 | Two water droplets combine to from a large drop in this process energy is | 11 |

978 | 11. The work done by the man is a. mgl b. mgh c. mg d. mg(l – h) | 11 |

979 | If ( A ) and ( B ) are two perpendicular vectors given by ( bar{A}=5 bar{i}+7 bar{j}+3 bar{k}, ) and ( 4 bar{B}= ) ( 2 bar{i}+2 bar{j}+c bar{k}, ) then the value of ( c ) is: ( A cdot-2 ) B. 8 ( c .-7 ) ( D cdot-8 ) | 11 |

980 | A certain force acting on a body of mass 2kg increase its velocity from 6m/s to ( 15 mathrm{m} / mathrm{s} ) in ( 2 mathrm{s} ). The work done by the force during this interval is? A. 27 B. 3J c. ( 94.5 mathrm{J} ) D. 1890 | 11 |

981 | Hall Hallo ” 25. If in the previous problem, we replace the man by a block of mass m and release it from top of the inclined plane, and let it gain a speed v, then a. W friction = -mgh + = mv b. W gravity = -mgh c. W friction = 0 d. W friction = – umgx, where x is the horizontal distance covered and u is the coefficient of friction between the block and the ground. | 11 |

982 | If ( vec{A}=2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to ( vec{B}=4 hat{j}-4 hat{i}+alpha hat{k}, ) then the value of ‘ ( alpha^{prime} ) is A . B. c. -1 D. ( frac{1}{-2} ) | 11 |

983 | Marbles, each of mass ( 1 mathrm{g} ) are dropped from a height of ( 10 mathrm{m} ) on to a horizontal smooth metal surface at the rate of 50 per second. Find the force on the surface. If the surface were inclined to the horizontal at an angle of ( 60^{circ}, ) what would be force on it be? Assume collisions to be elastic. ( g=9.8 m / s^{2} ) A. ( 1.2 N ; 0.7 N ) в. ( 1.4 N ; 0.5 N ) c. ( 1.4 N ; 0.7 N ) D. ( 0.4 N ; 0.4 N ) | 11 |

984 | A mass of ( 20 mathrm{kg} ) moving with a speed of ( 10 m / s ) collides with another stationary mass of 5 kg. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be ( mathbf{A} cdot 600 J ) в. ( 1000 J ) c. ( 800 J ) D. ( 1200 J ) | 11 |

985 | tilustration 8.8 Consider a variable force F=(3x + 5) N acting on a body and if it is displaced from x=2 m tox=4 m, calculate the work done by this force. | 11 |

986 | A force ( F ) acting on an object varies with distance ( x ) as shown in the figure. The work done by the force in moving the object from ( x=0 ) and ( x=20 m ) is A . ( 500 J ) B. ( 1000 J ) c. ( 1500 J ) D. ( 2000 J ) | 11 |

987 | The potential energy of a particle in a space is given by ( U=x^{2}+y^{2} ). Find the force associated with this potential energy: A ( .-2 x hat{i}-2 y hat{j} ) B . ( 2 x hat{i}-2 y hat{j} ) c. ( -2 x hat{i}+2 y hat{j} ) D. ( 2 x hat{i}+2 y hat{j} ) | 11 |

988 | Read the assertion and reason carefully to mark the correct option out of the options given below: Assertion: At height ( h ) from ground and at depth ( h ) below ground, where ( h ) is approximately equal to ( 0.62 R ) the value of ( g ) acceleration due to gravity is same. Reason: Value of ( g ) decreases both | 11 |

989 | An object is acted on by a retarding force of ( 10 N ) and at a particular instant its kinetic energy is ( 6 J . ) The object will come to rest after it has travelled a distance of: ( A cdot 3 ) ( frac{5}{5} mathrm{m} ) в. ( frac{5}{3} ) m c. ( 4 mathrm{m} ) D. 16 | 11 |

990 | A bullet of mass ( mathrm{m} ) is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by a distance d. Then the velocity of the bullet is : A. ( k d sqrt{M / m} ) в. ( frac{d}{M} sqrt{k m} ) c. ( frac{d}{m} sqrt{k M} ) D. ( frac{k M}{m} sqrt{d} ) | 11 |

991 | A body of mass 3 kg hits a wall at an angle of ( 600 & ) returns at the same angle. The impact time was0.2 s. Calculate the force exerted on the wall: A. ( 150 sqrt{3} N ) В. ( 50 sqrt{3} N ) c. ( 100 mathrm{N} ) D. ( 75 sqrt{3} N ) | 11 |

992 | A toy car of mass ( 5 mathrm{kg} ) moves up a ramp under the influence of force ( F ) plotted against displacement. The maximum height attained is given by A ( cdot y_{max }=20 mathrm{m} ) B ( cdot y_{max }=15 mathrm{m} ) ( mathbf{c} cdot y_{max }=11 m ) ( y_{max }=5 m ) | 11 |

993 | A freely falling body converts: A. kinetic energy into potential energy B. potential energy into kinetic energy C. chemical energy into kinetic energy D. potential energy into chemical energy | 11 |

994 | The block is moved from A to C along three different paths. Find the Work done by friction when the block is displaced from ( A ) to ( B ) and then from ( B ) to ( mathrm{C} ) A. ( W=-mu m g(a+b) ) в. ( W=-mu m g ) C. ( W=-mu m g(a+b) / 2 ) D. None of the above | 11 |

995 | A man of mass ( 50 mathrm{kg} ) falls freely from a height of ( 40 mathrm{m} ) into a swimming pool and just come to rest at the bottom of the pool. Assume that the average upward force on the man due to water is ( 1000 mathrm{N} . ) If depth of water in the pool is ( d ) then ( boldsymbol{d} ) is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) ) A. 20 B. ( 40 mathrm{m} ) ( c cdot 10 m ) ( D .5 mathrm{m} ) | 11 |

996 | A particle of mass m moving with a velocity v makes a head on elastic collision with another particle of the same mass initially at rest. The velocity of the first particle after collision is ( A ) B. ( v / 2 ) c. ( 2 v ) D. | 11 |

997 | A particle in a certain conservative force field has a potential energy given by ( U=frac{20 x y}{z} . ) The force exerted on it is? A ( cdotleft(frac{20 y}{z}right) hat{i}+left(frac{20 x}{z}right) hat{j}+left(frac{20 x y}{z^{2}}right) hat{k} ) B. ( -left(frac{20 y}{z}right) hat{i}-left(frac{20 x}{z}right) hat{j}+left(frac{20 x y}{z^{2}}right) hat{k} ) ( ^{mathrm{c}} cdotleft(frac{20 y}{z}right) hat{i}-left(frac{20 x}{z}right) hat{j}-left(frac{20 x y}{z^{2}}right) hat{k} ) D ( cdotleft(frac{20 y}{z}right) hat{i}+left(frac{20 x}{z}right) hat{j}-left(frac{20 x y}{z^{2}}right) hat{k} ) | 11 |

998 | A body falls from a height of 16 m and rebounds to a height of 4 m. The coefficient of restitution is A ( cdot frac{1}{4} ) B. ( frac{1}{2} ) ( c cdot frac{3}{4} ) D. | 11 |

999 | 85. A 500-kg car, moving with a velocity of 36 kmh on a straight road unidirectionally, doubles its velocity in 1 min. The average power delivered by the engine for doubling the velocity is a. 750 W b. 1050 W c. 1150 W d. 1250 W Tn11 | 11 |

1000 | A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the coefficient of restitution, then what will be the ratio of velocity of two balls after collision? A ( cdot frac{1-e}{1+e} ) в. ( frac{e-1}{e+1} ) c. ( frac{1+e}{1-e} ) D. ( frac{e+1}{e-1} ) | 11 |

1001 | A particle of mass ( m_{1} ) collides elastically with a stationary particle of ( operatorname{mass} boldsymbol{m}_{2}left(boldsymbol{m}_{1}>boldsymbol{m}_{2}right) . ) The maximum angle through which the striking particle may deviate as a result of the collision is given as ( sin theta_{1 max }=frac{x m_{2}}{m_{1}} ) Find ( boldsymbol{x} ) | 11 |

1002 | mg sinumg CUSO 52. The given plot shows the variation of U, the potential energy of interaction between two particles, with the distance separating them, r. UA ( BD C Fig. 8.243 1. B and D are equilibrium points. 2. C is a point of stable equilibrium. 3. The force of interaction between the two particles is attractive between points C and B, and repulsive between points D and E on the curve. 4. The force of interaction between the particles is repulsive between points C and A. Which of the above statements are correct? a. 1 and 3 b. 1 and 4 c. 2 and 4 d. 2 and 3 C 1 11 | 11 |

1003 | Illustration 8.23 In the previous illustration, consider the situation when the string is completely compressed. Then it begins to relax and will come to its original length. a. What is the work done by the spring during the period? b. Is the work done by the spring positive or negative? | 11 |

1004 | The amount of work done is pumping water out of a cubical vessel of height ( mathrm{m} ) is nearly (Given ( rho_{w a t e r}=1000 mathrm{kg} / mathrm{m}^{3} ) A . 5,000 в. 10,000 c. 5 J D. 10 J | 11 |

1005 | A bullet moving with a speed of ( 100 m s^{-1} ) canjust penetrate two planks of equal thickness. Then, the number of such planks penetrated by the same bullet when the speed is doubled will be: ( A cdot 6 ) B. 10 ( c cdot 4 ) D. | 11 |

1006 | A mass is suspended from the end of a spring. When the system is oscillating the amplitude of oscillation is ( 4 mathrm{cm} ) and the maximum kinetic energy of oscillation of the system is 1 joule. Then the force constant of the spring is: A. ( 2500 mathrm{N} / mathrm{m} ) в. ( 1250 mathrm{N} / mathrm{m} ) c. ( 500 mathrm{N} / mathrm{m} ) D. ( 250 mathrm{N} / mathrm{m} ) | 11 |

1007 | In elastic collision, ( A ) is conserved while in inelastic collision ( B ) is conserved. I.Momentum II.Kinetic Energy III.Potential Energy A. ( A= ) ।, ॥ ( B=1, ) II в. ( A= ) ।, ॥ ( B=1 ) c. ( A=| ) ( B= ) ॥, ॥ ॥ D. ( A=| ) ( B=1, ) II | 11 |

1008 | A sphere of mass ( 50 k g ) is attached by a second sphere of mass ( 90 mathrm{kg} ) with a force equal to a weight of ( 0.5 m g ) and their centres are ( 20 mathrm{cm} ) apart. The gravitational constant is. A ( .4 .2 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{2} ) B. ( 6.23 times 10^{-15} mathrm{Nm}^{2} mathrm{kg}^{2} ) c. ( 3.3 times 10^{-11} N m^{2} k g^{2} ) D. ( 4.4 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{2} ) | 11 |

1009 | Find the cosine of the angle between the vectors ( overrightarrow{boldsymbol{A}}=(mathbf{3} hat{boldsymbol{i}}+hat{boldsymbol{j}}+mathbf{2} hat{boldsymbol{k}}) boldsymbol{a n d} hat{boldsymbol{B}}= ) ( (2 hat{i}-2 hat{j}+4 hat{k}) ) A ( cdot frac{3}{sqrt{21}} ) B. ( frac{sqrt{12}}{sqrt{21}} ) c. ( frac{9}{sqrt{21}} ) D. ( frac{3}{sqrt{12}} ) | 11 |

1010 | Assertion Velocity time graph of two particles undergoing head-on collsion is shown in the figure. If collision is inelastic then value of y must be less than ( x ) Reason Coefficient of restitution(e) ( = ) velocity of |velocity of | 11 |

1011 | A billiard ball of mass ( M ) moving with velocity ( v_{1} ) collides with another ball of the same mass but at rest. If the collision is elastic the angle of divergence after the collision is A ( cdot 0^{circ} ) B. ( 30^{circ} ) ( c cdot 90^{circ} ) D. ( 45^{circ} ) | 11 |

1012 | A ( 30 g ) bullet initially travelling at ( 120 m / s ) penetrates ( 12 c m ) into a wooden block. The average resistance by the wooden block is A ( .2850 N ) в. 22000N c. ( 2000 N ) D. 1800N | 11 |

1013 | Which of the following statements about kinetic energy (K.E.) is true? A. All objects moving with the same velocity have the same K.E B. The K.E. of a body will quadruple if its velocity doubles C. As the velocity of a body increases, its K.E. decreases D. The K.E. of a body is independent of its mass | 11 |

1014 | (i) With reference to their direction of action, how does a centripetal force differ from a centrifugal force? (ii) State the Principle of conservation of energy. (iii) Name the form of energy which a body may possess even when it is not in motion. | 11 |

1015 | A bullet moving with a velocity of ( 200 mathrm{cm} / mathrm{s} ) penetrates a wooden block and comes to rest after traversing ( 4 mathrm{cm} ) inside it. What velocity is needed for travelling distance of ( 9 mathrm{cm} ) in same block A. ( 100 mathrm{cm} / mathrm{s} ) B. ( 136.2 mathrm{cm} / mathrm{s} ) c. ( 300 mathrm{cm} / mathrm{s} ) D. ( 250 mathrm{cm} / mathrm{s} ) | 11 |

1016 | Two bodies of unequal masses are dropped from the top of building. Which of the following is equal for both bodies at any instance? A. Speed B. Force of gravity c. Potential energy D. Kinetic energy | 11 |

1017 | How soon will the frame come to the orientation shown in figure (b) after collision? ( ^{A} cdot frac{pi l}{4 v} ) B. ( frac{7 pi l}{8 v} ) c. ( frac{pi l}{v} ) D. ( frac{7 pi l}{4 v} ) | 11 |

1018 | ( operatorname{mass} m=2 k g ) are connected to the ends of an ideal spring having force constant ( boldsymbol{k}=mathbf{1 0 0 0} boldsymbol{N m}^{-1} . ) System of these blocks and spring is placed on a rough floor. Coefficient of friction between blocks and floor is ( mu=0.5 ) Block B is pressed towards left so that spring gets compressed. Initial minimum compression ( boldsymbol{x}_{mathbf{0}} ) of spring such that block A leaves contact with the wall when system is released is: ( mathbf{A} cdot 3 mathrm{cm} ) B. ( 4 mathrm{cm} ) ( mathbf{c} .5 mathrm{cm} ) D. ( 6 mathrm{cm} ) | 11 |

1019 | A particle of mass ( m_{1} ) moving at certain velocity collides elastically head on with a particle of mass ( m_{2} ) at rest. After collision their velocities will be in the ratio of A ( cdot frac{m_{1}-m_{2}}{m_{1}+m_{2}} ) в. ( frac{m_{1}-m_{2}}{2left(m_{1}+m_{2}right)} ) c. ( frac{2 m_{1}}{m_{1}-m_{2}} ) D. ( frac{m_{1}-m_{2}}{2 m_{1}} ) | 11 |

1020 | The ( P E ) of a ( 2 k g ) particle, free to move along ( x ) -axis is given by ( V(x)= ) ( left(frac{x^{3}}{3}-frac{x^{2}}{2}right) J . ) The total mechanical energy of the particle is ( 4 J . ) Maximum speed ( left(operatorname{in} m s^{-1}right) ) is A ( cdot frac{1}{sqrt{2}} ) B. ( sqrt{2} ) c. ( frac{3}{sqrt{2}} ) D. ( frac{5}{sqrt{6}} ) | 11 |

1021 | The gravitational potential energy of an isolated system of three particles, each of mass ( m ), at the three corners of an equilateral triangle of side ( l ) is ( ^{text {A }}-frac{G m^{2}}{l} ) в. ( -frac{G m^{2}}{2 l} ) c. ( -frac{2 G m^{2}}{l} ) D. ( -frac{3 G m^{2}}{l} ) | 11 |

1022 | (ii) while climbing up a slope of height ( 10 mathrm{m}left(g=10 m s^{-2}right) ? ) A ( .5 k J^{2} ) ( begin{array}{ll}2 & text { 2 } \ text { 2 } & text { 2 }end{array} ) в. ( 50 k J ) c. ( 100 k J^{2} ) D. ( 5 k J ) | 11 |

1023 | A mass ( m_{1} ) moves with a grate velocity. It strikes another mass ( m_{2} ) at rest in head-on collision. It comes back along its path with low speed after collision. Then : ( mathbf{A} cdot m_{1}>m_{2} ) В. ( m_{1}<m_{2} ) ( mathbf{c} cdot m_{1}=m_{2} ) D. there is no relation between ( m_{1} ) and ( m_{2} ) | 11 |

1024 | The slope of kinetic energy and displacement curve for a particle in motion will be A. Equal to the acceleration of the particle B. Directly proportional to the acceleration of the particl C . Inversely proportional to the acceleration of the particle D. None of the above | 11 |

1025 | A bullet of mass ( m ) hits a target of mass ( M ) hanging by a string and gets embedded in it. If the block rises to a height ( h ) as a result of this collision, the velocity of the bullet before the collision is: A. ( v=sqrt{2 g h} ) B. ( v=sqrt{2 g h}left(1+frac{m}{M}right) ) c. ( v=sqrt{2 g h}left(1+frac{M}{m}right) ) D. ( v=sqrt{2 g h}left(1-frac{m}{M}right) ) | 11 |

1026 | Five particles each of mass ‘ ( m ) ‘ are kept at five vertices of a regular pentagon. A sixth particle of mass ‘ ( M^{prime} ) is kept at centre of the pentagon’ ( O ) ‘. Distance between ‘ ( M ) ‘ and ‘ ( m ) ‘ is ‘a’. Find (i) net force on ( ^{prime} boldsymbol{M}^{prime} ) (ii) magnitude of net force on ‘ ( M^{prime} ) if any one particle is removed from one of the vertices. | 11 |

1027 | If force ( overrightarrow{boldsymbol{F}}=4 hat{hat{boldsymbol{i}}}+5 hat{boldsymbol{j}} ) and displacement ( vec{S}=3 hat{i}+6 hat{j} ) then the work done is A ( .4 times 3 J ) B. ( 5 times 6 ) ( c cdot 6 times 3 ) D. ( 4 times 6 ) | 11 |

1028 | A bullet of mass ( 8 g ) strikes a vertical wooden plank ( 5 c m ) thick with a velocity of ( 200 m / s ) in a horizontal direction and emerges out of at ( 150 mathrm{m} / mathrm{s} ) in same direction find retarding force bullet experience in wood for what additional thickness bullet will just emerge on other side | 11 |

1029 | State and derive work energy theorem. | 11 |

1030 | A raised hammer possesses: A. K.E. only B. gravitational P.E. c. electrical energy D. sound energy | 11 |

1031 | Certain force acting on a ( 20 mathrm{kg} ) mass changes its velocity from ( 5 m s^{-1} ) to ( 2 m s^{-1} . ) Calculate the work done by the force A. ( -210 J ) B. ( 210 J ) c. -105 J. D. ( 420 J ) | 11 |

1032 | The angle made by the vector ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+ ) ( 3 hat{j} ) with ( y ) -axis is: A ( cdot tan ^{-1}left(frac{3}{2}right) ) B. ( tan ^{-1}left(frac{2}{3}right) ) c. ( sin ^{-1}left(frac{2}{3}right) ) D. ( cos ^{-1}left(frac{3}{2}right) ) | 11 |

1033 | A uniform solid sphere of mass ( mathrm{M} ) and radius ( R ) is kept on the horizontal surface. Find potential energy of the solid | 11 |

1034 | A bomb of ( 12 k g ) divides in two parts whose ratio of masses is ( 1: 3 . ) If kinetic energy of smaller part is ( 216 J ), then momentum of bigger part in ( k g- ) ( boldsymbol{m} / boldsymbol{s e c} ) will be A . 36 B. 72 c. 108 D. Data is incomplete | 11 |

1035 | A mass ( m ) moves with a velocity ( v ) and collides inelastically with another identical mass. After collision, the 1 st mass moves with velocity ( frac{v}{sqrt{3}} ) in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision A ( cdot frac{2 v}{sqrt{3}} ) B. ( frac{v}{sqrt{3}} ) ( ^{c} cdot sqrt{frac{2}{3}} ) D. The situation of the problem is not possible without external impulse | 11 |

1036 | There is an isolated planet having mass 2M and radius 2R, where M and R are the mass and radius of the earth. simple pendulum having mass ( mathrm{m} ) and length ( mathrm{R} ) is made to small oscillations on the planet. Find the time period of SHM of the pendulum in second. (Take ( left.pi=3.00, mathrm{g}=10 mathrm{m} / mathrm{s}^{2}, sqrt{2}=1.41right) ) A. 8000 B. 6768 s c. 9000 s D. 7968 s | 11 |

1037 | Two astronauts, each of mass ( 75 k g ), are floating next to each other in space, outside the space shuttle. They push each other through a distance of an arm’s length ( =1 m ) each with a force of ( 300 N ).If the final relative velocity of the two, w.r.t each other is ( V_{0} m / s, ) find the value of ( frac{left(V_{0}right)^{2}}{4}( ) Note that both astronauts are displaced by ( 1 boldsymbol{m} ) | 11 |

1038 | Find the velocity of a body of mass ( 100 g ) having a kinetic energy of ( 20 J ) | 11 |

1039 | The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of ( sqrt{3 g l} ). Find the angle rotated by the string before it becomes slack. | 11 |

1040 | A force acts on a ( 3 g ) particle in such a way that position of the particle as a function of time is given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}- ) ( 4 t^{2}+t^{3}, ) where ( x ) is in metre and ( t ) is in sec. The work done during the first ( 4 s ) is A. 570 mJ B. 450 mJ c. ( 490 mathrm{mJ} ) D. 528 mJ | 11 |

1041 | A ( 20 g ) bullet passes through a plate of mass ( 1 k g ) and finally comes to rest inside another plate of mass ( 2980 g ). It makes the plates move from rest to same velocity. The percentage loss in velocity of bullet between the plate is: ( A ) B . ( 50 % ) ( c .75 % ) D. ( 25 % ) | 11 |

1042 | If two forces ( boldsymbol{F}_{1}=mathbf{2} hat{mathbf{i}}+mathbf{4} hat{boldsymbol{k}} boldsymbol{F}_{2}=mathbf{3} hat{boldsymbol{j}}+ ) ( 2 hat{k} ) acts on one body and displaces it from (1,0,0) to (2,1,1) find net work done | 11 |

1043 | ‘lg. 8.206, the pulley shown is smooth. The spring and me string are light. Block B slides down from the top along mxed rough wedge of inclination e. Assuming that the block reaches the end of the wedge, find the speed block at the end. Take the coefficient of frict the block and the wedge to be u and that the spring was relaxed when the block was released from the top of the wedge. m B h w WWW Fig. 8.206 | 11 |

1044 | A solid cylinder of mass ( 2 mathrm{Kg} ) and radius ( 0.2 mathrm{m} ) is rotating about its own axis without friction with angular velocity 3 rad/s. A particle of mass 0.5 ( mathrm{Kg} ) and moving with a velocity of ( 5 mathrm{m} / mathrm{s} ) strikes the cylinder and sticks to it as shown in. The velocity of the system after the particle sticks it will be A. 0.3 radians/sec B. 5.3 radians/sec c. 10.3 radians/sec D. 8.3 Radians/sec | 11 |

1045 | DOOR 13 8 upwalu. Illustration 8.43 A block of mass m strikes a light pan fitted with a vertical spring after falling through a distance h. If the stiffness of the spring is k, find the maximum compression of the spring heelll -00000 Fig. 8.95 | 11 |

1046 | A smooth steel ball strikes a fixed smooth steel plate at an angle ( theta ) with the vertical. If ‘e’ is the coefficient of restitution, the angle at which the rebounce will take place with the vertical is A ( cdot alpha=tan ^{-1}left(frac{tan theta}{e}right) ) B. ( alpha=tan ^{-1}left(frac{cot theta}{e}right) ) c. ( _{alpha=tan ^{-1}left(frac{sin theta}{e}right)} ) D・ ( alpha=tan ^{-1}left(frac{e}{tan theta}right) ) | 11 |

1047 | A ball is bouncing down a flight of stairs. The coefficient of restitution is ( e ) The height of each step is ( d ) and the ball descends one step each bounce. After each bounce it rebounds to a height ( h ) above the next lower step. The height is large compared with the width of step so that the impacts are effectively head-on. Find the relationship between ( boldsymbol{h} ) and ( boldsymbol{d} ) A ( cdot h=frac{d}{1-e^{2}} ) в. ( h=frac{d}{1+e^{2}} ) c. ( h=frac{d}{1+e} ) D. ( h=sqrt{frac{d}{1-e^{2}}} ) | 11 |

1048 | A uniform rod of length ( L ) rests on a frictionless horizontal surface. The rod is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed ( v ) strikes the rod at its centre and becomes embedded in it. The mass of the bullet is one-sixth the mass of the rod. The ratio of the kinetic energy of the system before the collision to the kinetic energy of the bullet after the collision is ( frac{1}{x} . ) Find the value of ( x ) | 11 |

1049 | 22. What is the minimum value of x for which the ball can reach the point of projection after reaching C? a. 2Rb . SR c. 3R | 11 |

1050 | A body dropped freely from a height hon to a horizontal plane, bounces up and down and finally comes to rest.The coefficient of restitution is e. The ratio of velocities at the beginning and after two rebounds is A ( cdot 1: e ) B. e: ( c cdot 1: e^{3} ) D. ( e^{2}: 1 ) | 11 |

1051 | Assertion In elastic collision, kinetic energy is conserved. Reason Energy is always conserved. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion. B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion. C. Assertion is correct but Reason is incorrect. D. Both Assertion and Reason are incorrect. | 11 |

1052 | A particle of mass ( m_{1} ) moving with velocity ( v ) strikes with a mass ( m_{2} ) at rest, then the condition for maximum transfer of kinetic energy is : ( mathbf{A} cdot m_{1}>>m_{2} ) в. ( m_{2}>>m_{2} ) ( mathbf{c} cdot m_{1}=m_{2} ) D . ( m_{1}=2 m_{2} ) | 11 |

1053 | A ball of mass ‘m’ moving horizontally which velocity ‘u’ hits a wedge of mass ( M^{prime} . ) The wedge is situated on a smooth horizontal source. If after striking with wedge the ball starts moving in vertica direction and the wedge starts moving in horizontal plane. Calculated a) The velocity of wedge ( V ) b) The velocity (v) at which the ball moves in vertical direction. c) The impulse imparted by the ball on the wedge. d) The coefficient of restitution ( e=? ) | 11 |

1054 | The potential energy of a particle of mass ( 5 k g ) moving in the ( x ) -y plane is given by the equation, ( U=-7 x+24 y ) Joule. Here ( x ) and ( y ) are in the meter at ( boldsymbol{t}=mathbf{0}, ) the particle is at the origin and moving with velocity ( (2 i+3 j) m / s . ) The magnitude of the acceleration of the particle is: A ( .3 m / s^{2} ) в. ( 5 m / s^{2} ) c. ( 31 m / s^{2} ) D. ( 15 m / s^{2} ) | 11 |

1055 | A body of mass ( 3 mathrm{kg} ) is under a force which causes a displacement in it, given by ( s=t^{2} / 3(text { in } mathrm{m}) . ) Find the work done by the force in 2 second. A . 2 B . 3.8 c. 5.2 J D . 2.6 | 11 |

1056 | Assertion A body is moved from ( x=2 ) to ( x=1 ) under a force ( boldsymbol{F}=mathbf{4} boldsymbol{x} ), the work done by this force is negative. Reason Force and displacement are in opposite directions. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

1057 | Two particles of equal mass ( m ) go around in a circle of radius ( R ) under the action of their mutual gravitational attraction. The speed of each particle is ( v ). Find value of ( v ) ( ^{mathrm{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G m}right)} ) в. ( v=sqrt{left(frac{G m}{2 R}right)} ) c. ( v=frac{1}{2} sqrt{left(frac{G m}{R}right)} ) D. ( v=sqrt{left(frac{4 G m}{R}right)} ) | 11 |

1058 | A block of mass ( 10 mathrm{kg} ) is pulled by a constant horizontal force of ( 19 mathrm{N} ) and it is displaced by ( 15 mathrm{m} ) across the floor. Calculate the work done. A . 1.3 в. 30 J c. 285 J D. 5586 J E. 1 | 11 |

1059 | The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? A. Yes B. No c. Yes, at certain instants D. None of the above | 11 |

1060 | A body of mass travels in a straight line with a velocity ( v=k x^{3 / 2} ) where ( k ) is a constant. The work done in displacing the body from ( x=0 ) to ( x ) is proportional to: ( mathbf{A} cdot x^{1 / 2} ) B. ( x^{2} ) c. ( x^{3} ) D. ( x^{5 / 2} ) | 11 |

1061 | A ( 10 mathrm{kg} ) mass moves along ( mathrm{X} ) -axis. Its acceleration as a functions of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from ( x=0 ) to ( x=8 mathrm{cm} ? ) ( mathbf{A} cdot 8 times 10^{-2} J ) В. ( 16 times 10^{-2} J ) C. ( 4 times 10^{-4} J ) D. ( 1.6 times 10^{-3} J ) | 11 |

1062 | A ball of mass ( 4 mathrm{kg} ) moving on a smooth horizontal surface makes an elastic collision with another ball of mass ( mathrm{m} ) at rest in the line of motion of first ball, if after collision first ball moves in the same direction with one fourth of its velocity before collision, then mass of second ball is : ( A cdot 4 mathrm{kg} ) B. 4.4 kgg ( g g ) c. ( 2.4 mathrm{kg} ) D. ( 2 mathrm{kg} ) | 11 |

1063 | 87. In the above question, if equal forces are applied on two springs, then a. More work is done on Q b. More work is done on P c. Heir force constants will become equal d. Equal work is done on both the springs oo | 11 |

1064 | 41. If the total mechanical energy of the particle is 25 J, then it can be found in region a. -10<x<-5 and 6<x< 15 b. -10<x<0 and 6<x< 10 c. -5<x< 6 d. -10<x< 10 | 11 |

1065 | Which of the following statement is wrong for acceleration due to gravity. A. ( g ) decreases on going above the surface of earth B. ( g ) increases on going below the surface of earth ( mathrm{C} cdot g ) is maximum at pole D. ( g ) increases on going from equator to poles | 11 |

1066 | The potential energy of a body is given by ( U=A-B x^{2} ) (where ( x ) is the displacement). The magnitude of force acting on the particle is A. Constant B. Proportional to ( x ) c. Proportional to ( x^{2} ) D. Inversely proportional to | 11 |

1067 | Derive the expression for gravitational potential energy? | 11 |

1068 | A body moves a distance of ( 10 mathrm{m} ) long a straight line under the action of force of 5N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is: A . ( 0^{circ} ) B. ( 30^{circ} ) ( c cdot 60^{circ} ) D. ( 90^{circ} ) | 11 |

1069 | If a vector ( A ) is given as ( A=4 hat{i}+3 hat{j}+ ) ( 12 hat{k}, ) then the angle subtended with the x-axis is : ( ^{mathbf{A}} cdot sin ^{-1}left[frac{4}{13}right] ) B. ( sin ^{-1}left[frac{3}{13}right] ) ( ^{mathbf{c}} cdot cos ^{-1}left[frac{3}{13}right] ) D. ( cos ^{-1}left[frac{4}{13}right] ) | 11 |

1070 | A small ball moves toward right with a velocity ( v ). It collides with the wall and returns back and continues to and fro motion. If the average speed for first to and fro motion of the ball is ( (2 / 3) v, ) find the coefficient of restitution of impact. | 11 |

1071 | The speed of the block when it reaches the point ( Q ) is ( mathbf{A} cdot 5 m s^{-1} ) B. ( 10 m s^{-1} ) c. ( 10 sqrt{3} mathrm{ms}^{-1} ) D. ( 20 mathrm{ms}^{-1} ) | 11 |

1072 | Calculate the displacement for a body, if the workdone is ( 130 mathrm{J} ) and force applied is ( 19.5 mathrm{N} ) A. 6.66 m B. 130 ( m ) ( c .2535 mathrm{m} ) D. 20 ( m ) | 11 |

1073 | A ball of mass ( m ) is thrown vertically up with an initial velocity so as to reach a height ( h . ) The correct statement is: A. potential energy of the ball at the ground is ( m g h ) B. kinetic energy imparted to the ball at the ground is zero c. kinetic energy of the ball at the highest point is ( m g h ) D. potential energy of the ball at the highest point is ( m g h ) | 11 |

1074 | A mass ( m_{1} ) with initial speed ( v_{0} ) in the positive ( x ) -direction collides with a ( operatorname{mass} boldsymbol{m}_{2}=2 boldsymbol{m}_{1} ) which is initially at rest at the origin, as shown in figure. After the collision ( m_{1} ) moves off with speed ( boldsymbol{v}_{1}=boldsymbol{v}_{0} / 2 ) in the negative ( boldsymbol{y} ) direction, and ( m_{2} ) moves off with speed ( v_{2} ) at angle ( theta . ) Determine ( tan theta, ) and find ( v_{2} ) in terms of ( v_{0} ) | 11 |

1075 | A massless platform is kept on a light elastic spring, as shown in the figure. When particle of mass ( 0.1 mathrm{kg} ) is dropped on the pan from a height of ( 0.24 mathrm{m} ), the particle strikes the pan, and the spring is compressed by ( 0.01 mathrm{m} . ) From what height should the particle be dropped to cause a compression of ( 0.04 mathrm{m} ? ) A. ( 0.96 mathrm{m} ) B . ( 2.96 mathrm{m} ) c. 3.96 ( m ) D. ( 0.48 mathrm{m} ) | 11 |

1076 | A stick of mass ( mathrm{m} ) and length lis pivoted at one end and is displacement trough an angle ( theta ). The increase in potential energy is | 11 |

1077 | The distance of two planets from the Sun are ( 10^{13} ) and ( 10^{12} mathrm{m}, ) respectively. The ratio of time periods of these two planets is A. ( frac{1}{sqrt{10}} ) B. 100 c. ( frac{10}{sqrt{10}} ) D. ( sqrt{10} ) | 11 |

1078 | 6. In which of the following cases can the work done increase the potential energy? a. Both conservative and non-conservative forces b. Conservative force only c. Non-conservative force only d. Neither conservative nor non-conservative forces. | 11 |

1079 | 7. The extra power required is a. 0.4 W b. 0.08 W c. 0.04 W d. 0.2 W | 11 |

1080 | A car is moving at ( 100 mathrm{km} / mathrm{h} ). If the mass of the car is ( 950 k g ), its kinetic energy is: в. ( 0.367 M J ) c. ( 3.67 M J ) D. 3.67J | 11 |

1081 | In a tug of war, the team that exerts a larger tangential force on the ground wins, winning team not moving. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. Which of the following work is negative? A. work by the ground on the winning team. B. work done by string on the winning team. c. work by ground on the losing team. D. total external work on the two teams. | 11 |

1082 | The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point ( boldsymbol{P} ) be ( -5 J k g^{-1} . ) Suppose, we arbitrarily assume the gravitational potential at infinity to be ( +10 J k g^{-1} ), then the gravitational potential at ( boldsymbol{P} ) will be ( mathbf{A} cdot-5 J k g^{-1} ) ( mathbf{B} cdot+5 J k g^{-1} ) c. ( -15 J k g^{-1} ) ( mathbf{D} cdot+15 J k g^{-1} ) | 11 |

1083 | The force ( F ) acting on a particle moving in a straight line is shown below. What is the work done by the force on the particle in the 1st metre of the trajectory? ( A cdot 5 J ) В. ( 10 J ) ( c .15 J ) D. 2.5 5 | 11 |

1084 | If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{i}-4 hat{j}+alpha hat{k}, ) then the value of ( alpha ) is | 11 |

1085 | The graph of kinetic energy (K) of a body versus velocity (v) is represented as A. hyperbola B. parabola c. straight line D. none of these | 11 |

1086 | A chain of length ( L ) and mass ( m ) is placed upon a smooth surface. The length of BA is ( (boldsymbol{L}-boldsymbol{b}) ). Calculate the velocity of the chain when its end reaches B. B. ( 2 sqrt{frac{g sin theta}{L}}left(L^{2}-b^{2}right) ) c. ( sqrt{frac{g sin theta}{L}left(L^{2}-b^{2}right)} ) D. ( sqrt{frac{g sin theta}{2 L}}left(L^{2}-b^{2}right) ) | 11 |

1087 | The relation between displacement ( x ) and time ( t ) for a body of mass ( 2 K g ) moving under the action of a force is given by ( x=frac{t^{3}}{3}, ) where ( x ) is in meter and ( t ) in second, calculate the work done by the body in first 2 seconds. | 11 |

1088 | Expression for potential energy | 11 |

1089 | Two satellites ( A ) and ( B ) of masses ( m_{1} ) and ( m_{2}left(m_{1}=2 m_{2}right) ) are moving in circular orbits of radii ( r_{1} ) and ( r_{2}left(r_{1}=4 r_{2}right), ) respectively, around the earth. If their periods are ( T_{A} ) and ( T_{B} ) then the ratio ( T_{A} / T_{B} ) is A .4 B . 16 ( c cdot 2 ) D. 8 | 11 |

1090 | A force ( F=10 sqrt{2} N ) acts an angle of ( 45^{circ} ) above the horizontal on a ( 2 k g ) block placed on a rough horizontal surface. The coefficient of friction between the block and surface is 0.2 Find the work done by the force ( F ) on the block in ( 5 s ) initially the block is at rest. [Take ( g= ) ( left.mathbf{1 0} / boldsymbol{s}^{2}right] ) ( mathbf{A} cdot 250 J ) В. ( 2500 J ) c. ( 500 J ) D. ( 50 J ) | 11 |

1091 | If one body collides with another body of same mass at rest inelastically, the ratio of their speeds after collision shall be- ( A ) в. ( frac{1-e}{1+e} ) c. ( frac{1+e}{1-e} ) ( D cdot 1 ) | 11 |

1092 | Illustration 8.64 An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P, its position and instantaneous velocity changes w.rt, time assuming the automobile starts from rest. | 11 |

1093 | Let ( A, B ) and ( C ) are unit vectors suppose ( A . B=A . C=0 ) and angle between ( B ) and ( C ) is ( frac{pi}{6} ) then A ( . A=pm 2(B times C) ) B. ( A=pm sqrt{2}(B times C) ) c. ( A=pm 3(B times C) ) D. ( A=pm sqrt{3}(B times C) ) | 11 |

1094 | Two balls of equal masses are thrown upwards along the same vertical line at an interval of 2 seconds with the same initial velocity of ( 39.2 m s^{-1} . ) The total time of flight of each ball, if they collide at a certain height, and the collision is perfectly inelastic, will be A. ( 5 s ) and ( 3 s ) B. ( 10 s ) and ( 6 s ) c. ( 5 sqrt{15 s} ) and ( 3 sqrt{15 s} ) D. ( (5+sqrt{15}) s ) and ( (3+sqrt{15}) s ) | 11 |

1095 | Two forces whose magnitudes are in the ratio 3: 5 give a resultant of ( 28 N . ) If the angle of their inclination is ( 60^{circ} ), find the magnitude of each force. | 11 |

1096 | The angle ( theta ) between the vector ( p=hat{i}+ ) ( hat{j}+hat{k} ) and unit vector along ( x ) -axis is ( ^{A} cdot cos ^{-1}left(frac{1}{sqrt{3}}right) ) в. ( cos ^{-1}left(frac{1}{sqrt{2}}right) ) ( ^{mathrm{c}} cdot cos ^{-1}left(frac{sqrt{3}}{2}right) ) D. ( cos ^{-1}left(frac{1}{2}right) ) | 11 |

1097 | A force of ( 10 N ) is applied along ( x- ) axis calculate amount of work done to displace body from (2,3) to (-1,4) | 11 |

1098 | The flowing water of a river possesses energy. A. gravitational B. potential c. electrical D. kinetic | 11 |

1099 | Find the components of ( overrightarrow{boldsymbol{a}}=2 hat{boldsymbol{i}}+boldsymbol{3} boldsymbol{j} ) along the directions of vectors ( hat{i}+hat{j} ) and ( hat{mathbf{i}}-hat{boldsymbol{j}} ) | 11 |

1100 | The moving striker of the carom board will possess- – – energy A. Kinetic B. Potential c. solar D. Electric | 11 |

1101 | A water jet, whose cross sectional are is ‘a’ strikes a wall making an angle ‘ ( boldsymbol{theta}^{prime} ) with the normal and rebounds elastically. The velocity of water of density ‘d’ is v. Force exerted on wall is A ( cdot 2 a v^{2} d cos theta ) B. ( 2 a v^{2} d sin theta ) c. 2 avd ( cos theta ) D. avd cose | 11 |

1102 | A ( 30 mathrm{kg} ) child climbs 15 meters up a tree when he stops to have a look around. What is the child’s potential energy in joules? [Assume ( left.g=10 m / s^{2}right] ) A . 1500 B. 3000 c. 4500 D. 6000 | 11 |

1103 | Prove work energy theorem for a constant force. | 11 |

1104 | What is the work done by a force of ( 2 mathrm{N} ) in displacing a body by ( 2 mathrm{m} ) in the direction of the force? A ( cdot 4 J^{2} ) в. ( 6 J ) c. ( 4 J ) D. ( 48 J ) | 11 |

1105 | The work done by an external agent to shift a point mass from infinity to the centre of the earth is W. Then choose the correct relation. A. ( w=0 ) B. ( w>0 ) ( c cdot w<0 ) D. ( w leq 0 ) | 11 |

1106 | When a body of mass ( m_{1} ) moving with uniform velocity ( 40 m s^{-1} ) collides with another body of mass ( m_{2} ) at rest, then the two together begin to move with uniform velocity of ( 30 m s^{-1} . ) The ratio of the mass (i.e., ( frac{m_{1}}{m_{2}} ) ) of the two bodies will be A .1: 3 в. 3: 1 c. 1: 1.33 D. 1: 0.75 | 11 |

1107 | If ( g ) is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( boldsymbol{m} ) raised from the surface of the earth to a height equal to the radius ( R ) of the earth is ( ^{mathbf{A}} cdot frac{1}{2}^{m g R} ) в. ( 2 m g R ) ( ^{mathrm{c}} cdot frac{1}{4}^{m g R} ) D. ( m g R ) | 11 |

1108 | 1. TOULD 54. The potential energy function associated with the force E = 4 xyl + 2x² } is a. U=-2 xły b. U=-2xy + constant c. U = 2xy + constant d. Not defined 1 | 11 |

1109 | Assertion The change in kinetic energy of a particle is equal to the work done on it by the net force. Reason Change in kinetic energy of particle is equal to the work done only in case of a system of one particle. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

1110 | A body of volume ( V ) and density ( rho ) is raised through height ( h, ) in a liquid of density ( sigma(sigma<rho) . ) The increment in potential energy of the body is (Given acceleration due to gravity ( =g ) ): A. ( V rho g h ) в. V( sigma g h ) c. ( V(rho+sigma) g h ) D. ( V(rho-sigma) g h ) | 11 |

1111 | Two identical balls ( A ) and ( B ) are kept on a smooth table as shown. B collides with A with speed v. For different conditions mentioned in List I, match with speed of A after collision given in List II. | 11 |

1112 | By applying a force ( boldsymbol{F}=(mathbf{3} boldsymbol{x} boldsymbol{y}-mathbf{5} boldsymbol{z}) boldsymbol{j}+ ) ( 4 z k ) a particle is moved along the path ( boldsymbol{y}=boldsymbol{x}^{2} ) from point ( (boldsymbol{0}, boldsymbol{0}, boldsymbol{0}) ) to the point ( (2,4,0) . ) The work done by the ( F ) on the particle is (all values are in SI units) ( A ) в. ( frac{140}{5} J ) c. ( frac{232}{5} J ) D. | 11 |

1113 | A car is accelerating on a levelled plane and acquires a velocity 3 times of its initial velocity. During this process, the potential energy of the car A. does not change B. becomes 1.5 times that of initial potential energy c. becomes 3 times that of initial potential energy D. becomes 9 times that of initial potential energy | 11 |

1114 | The kinetic energy of a body of mass ( boldsymbol{m} ) moving with a velocity ( v ) is given by: A ( cdot m v^{2} ) в. ( frac{1}{2} m v^{2} ) ( mathrm{c} cdot 2 mathrm{mv}^{2} ) D. ( frac{1}{2} m^{2} v^{2} ) | 11 |

1115 | A vessel containing ( 50 k g ) of water of height ( 15 m ) is placed above the ground. Assuming the gravitational potential energy at ground to be zero. What will be the gravitational potential energy of water in the vessel ? ( left(boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-mathbf{2}}right) ) A . ( 0 . J ) в. ( 750 J ) c. ( 3750 J ) D. ( 7500 J ) | 11 |

1116 | A bullet fired into a trunk of a tree loses ( 1 / 4 ) of its kinetic energy in traveling a distance of ( 5 mathrm{cm} . ) Assuming constant retardation before stopping, it travels a further distance of A. ( 150 mathrm{cm} ) B. ( 1.5 mathrm{cm} ) c. ( 1.25 mathrm{cm} ) D. ( 15 mathrm{cm} ) | 11 |

1117 | A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of restitution is e: A ( cdot frac{1-e}{1+e} ) в. ( frac{e-1}{e+1} ) c. ( frac{1+e}{1-e} ) D. ( frac{e+1}{e-1} ) | 11 |

1118 | Illustration 8.38 The potential energy of configuration changes in x and y directions as U = kxy, where k is a positive constant. Find the force acting on the particle of the system as the function of x and y. | 11 |

1119 | 13. The speed y reached by a car of mass m in travelling a distance x, driven with constant power P, is given by 3xP (3xP)1/2 a. v= b. y= m m (3xP)1/3 (3xP) V= d. y = m | 11 |

1120 | The linear momentum of a particle is given by ( boldsymbol{P}=(boldsymbol{a} sin boldsymbol{t} hat{boldsymbol{i}}-boldsymbol{a} cos boldsymbol{t} hat{boldsymbol{j}}) ) kg- ( mathrm{m} / mathrm{s} ) A force ( overrightarrow{boldsymbol{F}} ) is acting on the particle Select correct alternative/s A. Linear momentum ( vec{P} ) of particle is always parallel to B. Linear momentum ( vec{P} ) of particle is always perpendicular to ( vec{F} ) c. Linear momentum ( vec{P} ) is always constant D. Magnitude of linear momentum is constant with respect to time | 11 |

1121 | If a ball is thrown upwards from the Surface of earth: A. The earth remains stationary while the ball moves upwards B. The ball remains stationary while the earth moves downwards C. The ball and earth both moves towards each other D. The ball and earth both move away from each other | 11 |

1122 | The decrease in potential energy between top position ( A ) and bottom position B is, ( =boldsymbol{m} boldsymbol{g} boldsymbol{r}-(-boldsymbol{m} boldsymbol{g} boldsymbol{r})=boldsymbol{2 m} boldsymbol{g} boldsymbol{r} quad ldots ) This must be equal to the increase in kinetic energy, when particle move from ( A ) to ( B ) i.e. ( frac{1}{2} boldsymbol{m} boldsymbol{v}_{2}^{2}-frac{1}{2} boldsymbol{m} boldsymbol{v}_{1}^{2} ) | 11 |

1123 | In the elastic collision of heavy vehicle moving with a velocity ( 10 mathrm{ms}^{-1} ) and a small stone at rest, the stone will fly away with a velocity equal to: A. ( 40 mathrm{ms}^{-1} ) B. 20 ( mathrm{ms}^{-1} ) ( c cdot 10 mathrm{ms}^{-1} ) ( D cdot 5 mathrm{ms}^{-1} ) | 11 |

1124 | 39. If the collision of ball with the building is elastic, then the angle with the horizontal at which the ball will rebound from the top of the building is a. 60° b. 45º c. 30° d. None | 11 |

1125 | 3. A force of F = 2xi +2j+3zÂ N is acting on a particle. Find the work done by this force in displacing the body from (1, 2, 3) m to (3, 6, 1) m. a. -10 J b . 100 J c. 10 J d. 1J | 11 |

1126 | A body of mass ( 0.2 mathrm{kg} ) dropped from a height ‘6 m’. If ( e=frac{1}{sqrt{6}} ) then K.E. lost during its first bounce from the ground is ( mathbf{A} cdot 1.96 J ) B. ( 9.8 J ) c. 19.6 .5 D. zero | 11 |

1127 | Q Type your question gas particles from both sides as shown in the figure. The solid dots are representing the molecules hitting from left side and the faint dots are the molecules hitting from right side. The mass of these gas particles is ( boldsymbol{m}= ) ( 10^{-26} k g ) and velocity before hitting is ( v_{0}=5 m / s . ) Volume density of the gas particles on both sides is ( n=10^{25} ) per ( m^{3} . ) Each beam has an area ( A=1 m^{2} ) and the collisions are perfectly elastic. What is the external force ( F ) (in newton) required to move the plate with a constant velocity ( boldsymbol{v}=2 boldsymbol{m} / boldsymbol{s} ) | 11 |

1128 | A body of mass ( 2 k g ) initially at rest moves under the action of an applied horizontal force of ( 7 N ) on a table with coefficient of kinetic friction ( =mathbf{0 . 1} ) Compute the Work done by the applied force in ( 10 s ) в. ( 890 J ) c. ( 1000 J ) D. ( 5000 J ) | 11 |

1129 | A particle moves along the ( x ) -axis from ( x=0 ) to ( x=5 m ) under the influence of a force ( F(text { in } N) ) given by ( F=3 x^{2}- ) ( 2 x+7 . ) Calculate the work done by this force | 11 |

1130 | An object of mass ( 5 k g ) falls from rest through a vertical distance of ( 20 m ) and attains a velocity of ( 10 mathrm{m} / mathrm{s} ). How much work is done by the resistance of air on the object? ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) A . ( 250 J ) В. ( -650 J ) c. ( -750 J ) D. ( 950 J ) | 11 |

1131 | An aeroplane flying in the sky possesses: A. Kinetic but not Potential Energy B. Potential but not Kinetic Energy C. Both Kinetic and Potential energy D. Neither Kinetic nor potential energy | 11 |

1132 | The angles which the vector ( vec{A}=3 hat{i}+ ) ( 6 widehat{j}+2 widehat{k} ) makes with the co-ordinate axes are: A ( cdot cos ^{-1} frac{3}{7}, cos ^{-1} frac{4}{7}, cos ^{-1} frac{1}{7} ) B. ( cos ^{-1} frac{3}{7}, cos ^{-1} frac{6}{7}, cos ^{-1} frac{2}{7} ) C ( cdot cos ^{-1} frac{4}{7}, cos ^{-1} frac{5}{7}, cos ^{-1} frac{3}{7} ) D. None of these | 11 |

1133 | A small ball is rolled with speed u from point A along a smooth circular track as shown in Fig. 8.281. If x = 3R, then X A — – B Reference level Fig. 8.281 21. Determine the required speed u so that the ball returns to A, the point of projection after passing through C, the highest point. 127 8. VER NININ | 11 |

1134 | If collision between the balls is completely inelastic, then : A. there is no loss of kinetic energy of the system B. entire kinetic energy of the system is lost C. kinetic energy loss in the system is less than 50% D. kinetic energy loss in the system is more than 50% | 11 |

1135 | Pick the odd one out from the following based on the nature of energy possessed by them. (moving car, water stored in a tank, a book on a table, ceiling fan in OFF position) | 11 |

1136 | Two balls ( A ) and ( B ) having masses ( m ) kg and ( 2 m mathrm{kg}, ) moving with speeds ( 21 mathrm{m} / mathrm{s} ) and ( 4 mathrm{m} / mathrm{s} ) respectively in opposite direction, collide head on. After collision ( A ) moves with a speed of ( 1 mathrm{m} / mathrm{s} ) in the same direction, then incorrect statement is : A. The velocity of B after collision is 6 ( mathrm{m} / mathrm{s} ) opposite to the direction before collision B. The coefficient of resitution is 0.2 c. The loss of kinetic energy due to collision is ( (200 mathrm{m}) ) ) D. The impulse of the force between the two ball is ( (40 mathrm{m}) ) Ns | 11 |

1137 | A body is hanging from a rigid support by an extensible string of length ( L ). It is struck inelastically by an identical body of mass ( m ) with horizontal velocity ( v= ) ( sqrt{2 g l}, ) the tension in the string increases just after striking by: A . ( m g ) в. ( 3 m g ) c. ( 2 m g ) D. None of these | 11 |

1138 | How much work is done in raising a stone of mass ( 5 mathrm{kg} ) and relative density 3 lying at the bed of a lake through height of 3 meter? (Take ( g=10 m s^{-2} ) ): A . 25 J B. 100 c. 75 J D. none | 11 |

1139 | Identify the mismatch of the following. A. Photo diode – optical signal B. LED – spontaneous emission C. Diode laser – stimulated emission D. Solar cell – electrical energy into light E. Photo conducting cell – photo detector | 11 |

1140 | How much work does a person do in pushing a box with a force of 20 N over a distance of ( 8.0 mathrm{m} ) in the direction of the force? A . 1.6 B . 16 J c. 160 D. 1600 E. 16000 | 11 |

1141 | State work-energy theorem. Prove it for a variable force. | 11 |

1142 | A chain of length ( l ) and mass ( m ) lies of the surface of a smooth hemisphere of radius ( R>1 ) with one end tied to the top of the hemisphere. Taking base of the hemisphere as reference line, find the gravitational potential energy of the chain. | 11 |

1143 | A rocket of initial mass 6000 kg ejects mass at a constant rate of ( 16 k g / s ) with constant relative speed of ( 11 k m / s ) What is the acceleration of the rocket a minute after the blast? (Neglect gravity) ( mathbf{A} cdot 28.7 mathrm{m} / mathrm{s}^{2} ) B . ( 34.9 mathrm{m} / mathrm{s}^{2} ) c. ( 39.4 mathrm{m} / mathrm{s}^{2} ) D. ( 27.8 mathrm{m} / mathrm{s}^{2} ) | 11 |

1144 | What are the advantages of wind energy? | 11 |

1145 | Three small bodies of identical masses can move along a straight line. The central body (2) is initially at rest and bodies 1 and 3 are at a distance ( L ) and ( 2 L ) from the central body respectively. Bodies 1 and 3 move towards body 2 with speeds ( v_{0} ) each. The collision between 1 and 2 is perfectly elastic and the collision between body 2 and 3 is perfectly inelastic. After all the collisions are over A. all the bodies come to rest B. the body 1 moves towards left, bodies 2 and 3 move towards right c. body 2 remains at rest and other bodies 1 and 3 turn back D. all the bodies move towards right. | 11 |

1146 | How is work done by a force measured when the force: (i) is in the direction of displacement. ( (i i) ) is at an angle to the direction of displacement. | 11 |

1147 | Three vectors ( vec{P}, vec{Q}, vec{R} ) are such that the ( |overrightarrow{boldsymbol{P}}|=|overrightarrow{boldsymbol{Q}}|,|overrightarrow{boldsymbol{R}}|=sqrt{mathbf{2}}|overrightarrow{boldsymbol{P}}| ) and ( overrightarrow{boldsymbol{P}}+overrightarrow{boldsymbol{Q}} ) ( +vec{R}=0 . ) The angle between ( vec{P} ) and ( vec{Q}, vec{Q} ) and ( vec{R} ) and ( vec{P} ) and ( vec{R} ) will be respectively. B . ( 90^{circ}, 45^{circ} ), ( 45^{circ} ) c. ( 45^{circ}, 90^{circ}, 90^{circ} ) D . ( 45^{circ}, 135^{circ}, 135^{circ} ) | 11 |

1148 | In above shown figure, a ball of mass 4 kg slides over frictionless surface and strikes the post with velocity of ( 1 mathrm{m} / mathrm{s} ) and rebounds toward the north at the same speed. The change in the magnitude of the eastward component of the momentum of the disk is: A. ( -4 k g-m / s ) в. ( -1 k g-m / s ) c. ( 0 k g-m / s ) D. ( 1 k g-m / s ) E . ( 4 k g-m / s ) | 11 |

1149 | A force is applied to box of mass ( 4 mathrm{kg} ) and it changes the velocity from ( 3 mathrm{m} / mathrm{s} ) to ( 6 mathrm{m} / mathrm{s} ) in ( 8 mathrm{s} ). Determine the work done by force during the this process. A . 27 J B. 54 J c. 72 J D. 96 J E. cannot be determined from the information given | 11 |

1150 | Initial speed of the bullet is A ( .549 m / s ) B. ( 502 m / s ) c. ( 475 mathrm{m} / mathrm{s} ) D. ( 624 mathrm{m} / mathrm{s} ) | 11 |

1151 | Consider elastic collision of a particle of mass ( m ) moving with a velocity ( u ) with another particle of the same mass at rest. After the collision the projectile and the stuck particle move in directions making angles ( theta_{1} ) and ( theta_{2} ) respectively with the initial direction of motion. The sum of the angles ( boldsymbol{theta}_{1}+boldsymbol{theta}_{2} ) is | 11 |

1152 | If ( vec{A} cdot vec{B}=vec{A} times vec{B}, ) then angle between ( vec{A} ) and ( vec{B} ) is A . 45 B. 30 ( c cdot 60^{circ} ) D. ( 90^{circ} ) | 11 |

1153 | A proton moving with a velocity of ( 1.25 times 10^{5} mathrm{m} / mathrm{s} ) collides with a stationary helium atom. The velocity of proton after collision is ( mathbf{A} cdot 0.75 times 10^{5} m s^{-1} ) B . ( 7.5 times 10^{5} mathrm{ms}^{-1} ) c. ( -7.5 times 10^{5} mathrm{ms}^{-1} ) D. ( 0 m s^{-1} ) | 11 |

1154 | Two balls initially moving in same direction with speed ( 10 m s^{-1} ) and ( 5 m s^{-1} ) make a head-on collision. After collision, they move with speed ( 4 m s^{-1} ) and ( 6 m s^{-1} ) in the same direction. Coefficient of restitution of collision is : A . 0.2 B. 0.4 ( c cdot 0.6 ) D. 0.8 | 11 |

1155 | The atmospheric pressure and height of barometer column is ( 10^{5} P_{a} ) and ( 760 mathrm{mm} ) respectively on the earth surface. If the barometer is taken to moon then column height will be A . zero B. 76 mm c. ( 126.6 mathrm{mm} ) D. 760 mm | 11 |

1156 | Two identical blocks ( A ) and ( B ), each of mass ‘m’ resting on a smooth horizontal surface, are inter connected by spring of stiffness ‘K’. If the block B is acted on by a horizontal force ‘ ( mathrm{F}^{prime} ) and the elongation of the spring is ‘e’, the relative acceleration between the blocks is equal to A ( cdot frac{F}{2 m} ) B. ( frac{F-K e}{m} ) ( mathbf{c} cdot frac{F-2 K e}{m} ) D. ( frac{K e}{m} ) | 11 |

1157 | The kinetic energy acquired by a mass ( mathrm{m} ) after travelling a fixed distance from rest under the action of constant force is A. directly proportional to velocity. B. directly proportional to m. c. independent of m. D. inversely proportional to ( mathrm{m} ). | 11 |

1158 | A force ( F=left(3 x^{2}+2 x-7right) N ) acts on a ( 2 k g ) body as a result of which the body gets displaced from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{5} boldsymbol{m} ) The work done by the force will be: A . ( 5 . J ) B. ( 70 J ) ( mathrm{c} .115 mathrm{J} ) D. ( 270 J ) | 11 |

1159 | An automobile engine propels a ( 1000 mathrm{kg} ) car ( A ) along a leveled road at a speed of ( 36 k m h^{-1} . ) The frictional force is 100 N. Suppose after traveling a distance of ( 200 mathrm{m}, ) this car collides with another stationary car ( mathrm{B} ) of the same mass and comes to rest. Let Its engine also stop at the same time. Now, car B starts moving on the same level road without getting its engine started. Find the speed of the car B just after the collision. A. ( 36 mathrm{km} / mathrm{h} ) B. 72 km/h ( mathbf{c} cdot 18 mathrm{km} / mathrm{h} ) D. ( 100 mathrm{km} / mathrm{h} ) | 11 |

1160 | 2. Which one is correct? a. Both masses will have equal KE. b. Lighter block will have greater KE. c. Heavier block will have greater KE. d. None of above answers is correct. | 11 |

1161 | Which of the following possesses potential energy? A. Moving vehicle on the road B. A running athlete c. Stone on the road D. A stretched rubber band | 11 |

1162 | Find the projection of ( vec{A}=2 hat{i}-hat{j}+ ) ( hat{boldsymbol{k}} quad boldsymbol{o} boldsymbol{n} quad overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}-boldsymbol{2} hat{boldsymbol{j}}+hat{boldsymbol{k}} ) ( A cdot frac{5}{sqrt{6}} ) B. ( frac{7}{10} ) ( c cdot frac{6}{sqrt{5}} ) D. ( $ $ ) frac ( {5 text { ) ( } mid text { sqre }{3}} ) | 11 |

1163 | A uniform chain of length ( 2 m ) is kept on a table such that a length of ( 50 mathrm{cm} ) hangs freely from the edge of the table. The total mass of the chain is ( 5 k g . ) What is the work done in pulling the entire chain on the table. (in J) A . 7.2 B. 3 c. 4.6 D. 12 | 11 |

1164 | A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a. varies with time t as a = krt, where k is a constant. The power delivered to the particles by the force acting on it is (IIT JEE, 1987) b. mk?r?t d. Zero a. 2tmk?r?t (mkt p215) | 11 |

1165 | A satellite is revolving round the earth with orbital speed ( v_{0} ). If it is imagined to stop suddenly, the speed with which it will strike the surface of the earth would be ( left(v_{e}- ) escape speed of a body from right. earth’s surface) A ( cdot frac{v_{e}^{2}}{v_{0}} ) в. ( v_{0} ) c. ( sqrt{v_{e}^{2}-v_{0}^{2}} ) D. ( sqrt{v_{e}^{2}-2 v_{0}^{2}} ) | 11 |

1166 | 62 Block A is hanging from a vertical spring and is at rest. Block B strikes block A with velocity v and sticks to it. Then the value of v for which the spring just attains natural length is m in Fig. 8.247 (60mg² a. V k b. som? a. 10mg? C. V d. None of these | 11 |

1167 | A bag of wheat weighs 100 kg. To what height should it be raised, so that its potential energy may be ( 9800 mathrm{J}(g= ) ( left.9.8 m s^{-2}right) ) | 11 |

1168 | A homogeneous rod ( X Y ) of length ( L ) and mass ( M ) is pivoted at the centre ( C ) such that it can rotate freely in the vertical plane. Initially, the rod is in the horizontal position. A blob of wax of same mass ( M ) as that of the rod falls vertically with the speed ( V ) and sticks to the rod midway between points ( C ) and ( Y . ) If the rod rotates with angular speed ( omega ) what will be angular speed in terms of ( boldsymbol{V} ) and ( boldsymbol{L} ) ? | 11 |

1169 | At what height above the ground must a mass of ( 5 mathrm{kg} ) be to have its P.E. equal in value to the K.E. possessed by it when it moves with a velocity of ( 10 mathrm{m} / mathrm{s} ? ) (Assume ( boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2} ) A. ( 1 mathrm{m} ) B. ( 5 mathrm{m} ) ( c cdot 10 m ) D. 50 ( m ) | 11 |

1170 | A force of ( 5 mathrm{N}, ) making an angle ( theta ) with the horizontal, acting on an object displaces it by ( 0.4 mathrm{m} ) along the horizontal direction. If the object gains kinetic energy of 1 J, the horizontal component of the force is? A . ( 1.5 mathrm{N} ) в. 2.5 N c. 3.5 N D. 4.5 N | 11 |

1171 | Assertion The angle between the two vectors ( (hat{i}+ ) ( hat{boldsymbol{j}}) ) and ( (hat{boldsymbol{j}}+hat{boldsymbol{k}}) ) is ( frac{pi}{3} ) radian Reason Angle between two vectors ( vec{A} ) and ( vec{B} ) given by ( boldsymbol{theta}=cos ^{-1}left(frac{vec{A} cdot vec{B}}{A B}right) ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

1172 | Why are shockers used in scooters and cars? Explain. A. decreases friction B. Increase the time of impact c. increases friction D. decorative | 11 |

1173 | Energy required to break a bond of DNA is approximately ( A cdot-1 e V ) B. 0.1 ev c. ( sim 0.01 mathrm{ev} ) D. 2.1 ev | 11 |

1174 | 24. A toy gun uses a spring of force constant K. Before being triggered in the upward direction, the spring is compressed by a distance x. If the mass of the shot is m, on being triggered, it will go up to a maximum height of Kr? b. *? mg Kmg R2 d. Kºr? 2mg mg | 11 |

1175 | The assembly of two discs as shown in figure is placed on a rough horizontal surface and the front disc is given an initial angular velocity ( omega_{0} ) Determine the final linear and angular velocity when both the discs start rolling. It is given that friction is sufficient 10 sustain rolling in the rear wheel from the starting of motion | 11 |

1176 | What happened when a rubber band is stretched? | 11 |

1177 | What is work done in holding a body of mass ( 20 mathrm{kg} ) at a height of ( 2 mathrm{m} ) above the ground? ( left(g=10 m / s^{2}right) ) A . ( 40 mathrm{J} ) B. 400 J c. ( 10 J ) D. zero | 11 |

1178 | A bullet is fired from a rifle. If rifle recoils freely, then K.E. of the rifle is: A. less than that of the bullet B. more than that of the bullet c. same as that of the bullettet D. equal or less than that of the bullet | 11 |

1179 | Assertion Two particles moving in the same direction do not lose all their energy in a completely inelastic collision Reason Principle of conservation of momentum holds true for all kinds of collision A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

1180 | A skater of mass m standing on ice throws a stone of mass M with a velocity of ( V ) in a horizontal direction. The distance over which the skater will move back (the coefficient of friction between the skater and the ice is ( mu ) ): ( ^{mathbf{A}} cdot frac{M^{2} V^{2}}{2 m mu g} ) в. ( frac{M V^{2}}{2 m^{2} mu g} ) ( ^{mathrm{c}} cdot frac{M^{2} V^{2}}{2 m^{2} mu g} ) D. ( frac{M^{2} V^{2}}{2 m^{2} mu^{2} g} ) | 11 |

1181 | A 50 gram bead slides on a frictionless wire as shown above. At what point on the wire will the bead come to a complete stop? The initial speed at ( C ) is ( sqrt{2 g h} ) A. Point ( A ) B. Point B c. Point ( c ) D. Point D E. Point E | 11 |

1182 | During collision a) There is a change in momenta of individual bodies b) The change in total momentum of the system of colliding particle is zero c) The change in total energy is zero d) The law of conservation of momentum is not valid A. only a ( & ) b are true B. only b & c are true ( c cdot a, b & c ) are true D. b, c & d are true | 11 |

1183 | An athelete diving off a high spring board can perform a variety of physical moments in the air before entering the water below. Which one of the following parameters will remain constant during the fall? The athelete’s: A. linear velocity B. linear momentum c. moment of inertia D. angular momentum | 11 |

1184 | If vector ( vec{A}=hat{i}+c hat{j}+5 hat{k} ) and vector ( vec{B}=2 hat{i}+hat{j}-hat{k} ) are perpendicular,then calculate the value of ( c ) | 11 |

1185 | A bead of mass ( mathrm{m} ) kept at the top of a smooth hemispherical wedge of mass M and radius R, is gently pushed towards right. As a result, the wedge slides due left. Find the a. speed of the wedge b. magnitude of velocity of the bead relative to the wedge | 11 |

1186 | An object is dropped from a height ( h ) from the ground. Every time it his the ground it looses ( 50 % ) of its kinetic energy. The total distance covered as ( rightarrow infty ) is: ( mathbf{A} cdot 2 h ) B . ( infty ) c. ( frac{5}{3} h ) D. ( frac{8}{3} h ) | 11 |

1187 | If there is a nonzero net force acting on an object for some time, which of the following must be true? I. The object is gaining kinetic energy II. The object experiences displacement III. There is work being done on the object A. I only B. I and II only c. I and III only D. Il and III only E . I, II, and III | 11 |

1188 | A box of mass ( mathrm{m} ) slides down a frictionless inclined plane of Iength L and vertical height h. Calculate the kinetic energy at the bottom of plane. A . mgl в. mghh c. ( mathrm{mgL} / mathrm{h} ) D. ( operatorname{mgh} / mathrm{L} ) E. mghL | 11 |

1189 | 49. A particle is projected along a horizontal field whose coefficient of friction varies as u = AIV, where r is the distance from the origin in metres and A is a positive constant. The initial distance of the particle is 1 m from the origin and its velocity is radially outwards. The minimum initial velocity at this point so the particle never stops is a.. b. 2./8A c. √28A d. 4/qA T I LIA Daca lacadan tune inclinad | 11 |

1190 | The mass of a spaceship is 1000 kg. It is to be launched from the earths surface out into free space. The value of ( g ) and ( R(text { radius of earth) are } 10 m / s ) and ( 6400 mathrm{km} ) respectively. The required energy for this work will be: A ( cdot 6.4 times 10^{11} J ) ( J ) В. ( 6.4 times 10^{8} J ) c. ( 6.4 times 10^{9} J ) D. ( 6.4 times 10^{10} J ) | 11 |

1191 | Find the components of vector ( overrightarrow{boldsymbol{a}}=mathbf{3} hat{mathbf{i}}+ ) ( 4 hat{j} ) along the direction of vectors ( hat{i}+hat{j} & ) ( hat{mathbf{i}}-hat{boldsymbol{j}} ) A ( cdot frac{7}{2}(hat{i}+hat{j}),-frac{1}{2}(hat{i}-hat{j}) ) B ( cdot frac{1}{2}(hat{i}+hat{j}),-frac{7}{2}(hat{i}-hat{j}) ) c. ( frac{-7}{2}(hat{i}+hat{j}),-frac{1}{2}(hat{i}-hat{j}) ) D ( cdot frac{7}{2}(hat{i}+hat{j}), frac{1}{2}(hat{i}-hat{j}) ) | 11 |

1192 | Hail storms are observed to strike the surface of the frozen lake at 30 with the vertical and rebiund at 60 with the vertical. Then: | 11 |

1193 | What is the angle between vector ( vec{A}= ) ( hat{mathbf{i}}+hat{mathbf{j}}+sqrt{mathbf{2}} hat{boldsymbol{k}} ) and the z-axis : A ( cdot 0^{circ} ) B . 45 ( c cdot 60 ) D. ( 90^{circ} ) | 11 |

1194 | A uniform disc of mass ( m ) is fitted (pivoted smoothly) with a rod of mass ( m / 2 . ) If the bottom of the rod is pulled with a velocity ( v, ) it moves without changing its angle of orientation and the disc rolls without sliding. Find the kinetic energy of the system ( (r o d+ ) ( operatorname{disc} ) | 11 |

1195 | A non-zero vector ( vec{a} ) is parallel to the line of intersection of the plane ( boldsymbol{P}_{1} ) determined by ( hat{i}+hat{j} ) and ( hat{i}-2 hat{j} ) and plane ( P_{2} ) determined by vector ( 2 hat{i}+ ) ( hat{j} ) and ( 3 hat{i}+2 hat{k}, ) then angle between ( vec{a} ) and vector ( hat{i}-2 hat{j}+2 hat{k} ) is A ( cdot frac{pi}{4} ) в. ( c cdot frac{pi}{3} ) D. ( pi ) | 11 |

1196 | Match the following list 1 to list 2 | 11 |

1197 | If ( R ) is radius of the earth and ( W ) is work done in lifting a body from the ground to an altitude ( R ), the work which should be done in lifting it further to twice that altitude is: A ( cdot frac{W}{2} ) B. ( W ) c. ( frac{W}{3} ) D. ( 3 W ) | 11 |

1198 | A body falling from a height of ( 10 m ) rebounds from hard floor. If it loses ( 20 % ) energy in the impact, then coefficient of restitution is A . 0.89 B. 0.56 c. 0.23 D. 0.18 | 11 |

1199 | Three identical point masses, each of mass ( 1 k g ) lie in the ( x ) -y plane at points ( (0,0),(0,0.2 m) ) and ( (0.2 m, 0) . ) The gravitational force on the mass at the origin is A ( cdot 1.67 times 10^{-9}(hat{i}+hat{j}) N ) B. ( 3.34 times 10^{-10}(hat{i}+hat{j}) N ) c. ( 1.67 times 10^{9}(hat{i}-hat{j}) N ) D. ( 3.34 times 10^{10}(hat{i}-hat{j}) N ) | 11 |

1200 | Given ( overline{boldsymbol{a}}+overline{boldsymbol{b}}+overrightarrow{boldsymbol{c}}+overline{boldsymbol{d}}=mathbf{0}, ) which of the following statements is/are not a correct statement? A ( cdot vec{a}, vec{b}, vec{c} ) and ( vec{d} ) must be a null vector. B. The magnitude of ( ( vec{a}+vec{c} ) ) equals the magnitude of ( a(vec{b}+vec{d}) ) C. The magnitude of ( vec{a} ) can never be greater than the summ of the magnitudes of ( vec{b}, vec{c} ) and ( vec{d} ) D. ( b+vec{c} ) must He in the plane of ( vec{a} ) and ( vec{d} ) if ( vec{a} ) and ( vec{d} ) are not collinear and in the line of ( vec{a} ) and ( bar{d} ), if they are collinear. | 11 |

1201 | Show that kinetic energy is always lost in inelastic collision. | 11 |

1202 | An object mass ( 10 mathrm{kg} ) falls from rest through a vertical distance of ( 10 mathrm{m} ) and acquires a velocity of ( 10 mathrm{m} / mathrm{s} ). The work done by the push of air on the object is ( left(g=10 m / s^{2}right) ) A. 500 J B . -500 J c. 250 D . -250J | 11 |

1203 | A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is given an initial velocity of ( 4 m s^{-1} ) by applying a force. The trolley comes to rest after traversing a distance of ( 16 mathrm{m} ) How much work is done on the trolley? A. ० B. 320 J c. ( 120 mathrm{J} ) D. 250 J | 11 |

1204 | Calculate the work required to be done to stop a car of ( 1500 mathrm{kg} ) moving at a velocity of ( 60 mathrm{kmh}^{-1} ) в. 208333 Л c. -209333 J D. ( -207333 J ) | 11 |

1205 | The gravitational force between two objects is proportional to ( frac{1}{R} ) (and not as ( left.frac{1}{R^{2}}right) ) where ( R ) is separation between them then a particle in a circular orbit under such a force would have its orbital speed ( nu ) proportional to A ( cdot frac{1}{R^{2}} ) B . ( R^{0} ) c. ( R^{text {। }} ) D. ( frac{1}{R} ) | 11 |

1206 | Vector ( vec{a} ) has components ( boldsymbol{a}_{boldsymbol{x}}=mathbf{3}, boldsymbol{a}_{boldsymbol{y}}= ) 4. Find the components of a vector ( overrightarrow{boldsymbol{c}} ) which is perpendicular to ( vec{a} ) and has a magnitude of 5 units. A ( cdot c_{x}=pm 4, c_{y}=mp 3 ) B . ( c_{x}=pm 3, c_{y}=mp 4 ) C ( cdot c_{x}=pm 2, c_{y}=mp 3 ) D. ( c_{x}=pm 3, c_{y}=mp 2 ) | 11 |

1207 | A mass ( m ) is thrown vertically upward into air with initial speed ( u . ) A constant force ( F ) due to air resistance acts on the mass during it’s travel. Taking into account the work done against air drag, the maximum distance covered by the mass to reach the top is (Given acceleration due to gravity ( =g ) ) A ( cdot frac{u^{2}}{2 g} ) в. ( frac{u^{2}}{2 g+2 F / m} ) с. ( frac{u^{2}}{2 g+F / m} ) D. ( frac{u^{2}}{g+F / m} ) | 11 |

1208 | external = AX +20 Illustration 8.40 A block is placed on the top of a plane inclined at 37° with horizontal. The length of the plane is 5 m. The block slides down the plane and reaches the bottom. 5 m 37° Fig. 8.90 a. Find the speed of the block at the bottom if the inclined plane is smooth. b. Find the speed of the block at the bottom if the coefficient of friction is 0.25. | 11 |

1209 | Two balls ( A ) and ( B ) having masses ( 1 k g ) and ( 2 k g ) moving with speeds ( 21 m / s ) and ( 4 m / s ) respectively in opposite direction, collide head on. After collision ( A ) moves with a speed of 1 m/ ( s ) in the same direction, then the coefficient of restitution is : A . 0.1 B. 0.2 c. 0.4 D. None | 11 |

1210 | Two small particles of equal masses start moving in opposite directions from a point ( A ) in a horizontal circular orbit. Their tangential velocities are ( boldsymbol{v} ) and ( 2 v ) respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at ( A ), these two particles will again reach the point ( A ) ? A . 4 B. 3 ( c cdot 2 ) D. | 11 |

1211 | What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer. | 11 |

1212 | Which of the following graphs depicts the variation of ( mathrm{KE} ) of a ball, bouncing on a horizontal floor with height? (neglect air resistances) ( A ) B. ( c ) D. None of these | 11 |

1213 | the value of ( x ) at which ( F_{x} ) is zero. ( A cdot x=2 m ) B. ( x=4 ) m ( c cdot x=6 m ) D. ( x=8 ) m | 11 |

1214 | 10. In Fig. 8.304, find the velocity of m, in ms when m2 falls by 9 m. u = 0.1 m m2 Fig. 8.304 = m; m2 = 2m (take g = 10 ms?). Given m | 11 |

1215 | Q Type your question ( M_{A}=2 M ) and ( M_{B}=M, ) as indicated in the figure. The two masses are initially oriented along the Y-axis and connected by a rod of negligible mass of length ( mathrm{D} ), forming a rigid body. A force of magnitude ( boldsymbol{F}=|overrightarrow{boldsymbol{F}}| ) along the X-axis is applied to the object at ( mathrm{B} ) at ( t=0 ) for ( mathrm{a} ) short time interval ( delta t . ) Neglect gravity. The expression for the magnitude of angular velocity of the system after the collision is: A ( cdot frac{F delta t}{M D D} ) в. ( frac{2 F delta t}{3 M D} ) c. ( frac{F delta t}{2 M D} ) D. ( frac{3 F delta t}{2 M D} ) | 11 |

1216 | A bullet fired into a fixed target loses half of its velocity after penetrating ( 3 mathrm{cm} ) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion? ( mathbf{A} .3 .0 mathrm{cm} ) B. ( 2.0 mathrm{cm} ) c. ( 1.5 mathrm{cm} ) D. ( 1.0 mathrm{cm} ) | 11 |

1217 | A ball of mass m makes perfectly elastic head-on collision with a ball of mass nm which is initially at rest. Show that the fractional transfer of energy by the first ball is ( 4 n /(1+n)^{2} . ) Deduce the value of ( n ) for which the transfer is maximum. | 11 |

1218 | A sphere of mass ( m_{1}=2 k g ) collides with a sphere of mass ( m_{2}=3 k g ) which is at rest. Mass ( m_{1} ) will move at right angles to the line,joining centres at the time of collision, if the coefficient of restitution is : ( A cdot 4 / 9 ) в. ( 1 / 2 ) ( c cdot frac{2}{3} ) D. ( sqrt{2 / 3} ) | 11 |

1219 | Identify the energy changes in the following two cases – ( A: A ) car moving up a hill B : Photographic film is exposed to sun- light A. In ‘A’ mechanical energy in moving car is converted to potential energy and in ‘B’ potential energy is converted to chemical energy B. In’A’ potential energy in moving car is converted to kinetic energy and in ‘B’ chemical energy is converted to light energy. C. In’A’ kinetic energy in moving car is converted to potential energy and in ‘B’ potential energy is converted to light energy. D. In’A’ kinetic energy is moving car is converted to potential energy and in ‘B’ light energy is converted to chemical energy. | 11 |

1220 | 10. A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ar. Here k and a are positive constants. For x > 0, the functional form of the potential energy U (x) of the particle is (IIT JEE, 2002) U(x) b. U(x) U(x) ► d. | 11 |

1221 | A uniform chain of length ( 2 m ) is kept on a table such that a length of ( 60 mathrm{cm} ) hanging freely from the edge of the table. The total mass of the chain is ( 4 k g . ) The work done is pulling the entire chain on the table (Take ( left.g=m s^{-2}right) ) A . ( 12.9 J ) B. ( 6.3 J ) c. ( 3.6 J ) D . ( 2.0 J ) | 11 |

1222 | Find out the potential energy of the force ( boldsymbol{F}=boldsymbol{y} hat{boldsymbol{i}}+boldsymbol{x} hat{boldsymbol{j}} boldsymbol{N} ) A. ( -x y+c ) B. ( x y+c ) c. ( -x y-c ) D. ( x y-c ) | 11 |

1223 | Suppose a ball of mass ( mathrm{m} ) is thrown vertically upward with an initial speed ( v ) Its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentums of the ball are same. Is this an example of conservation of momentum? A. Yes B. No c. Sometimes D. None of these | 11 |

1224 | Maximum velocity of block during subsequent motion of the system after release of ball is : A ( cdot[g L(1-cos theta)]^{1 / 2} ) B ( cdot[2 g L(1-cos theta)]^{1 / 2} ) ( mathbf{c} cdot[g L(cos theta)]^{1 / 2} ) D. insufficient information | 11 |

1225 | An object of mass 40 kg having velocity ( 4 hat{text { ì }} m / s ) collides with another objects of mass 40 kg having velocity ( 3 hat{i} ). If the collision is perfectly inelastic, then the loss of mechanical energy. ( A ). ( 250 J ) B. 100 c. 125 D. 35 J | 11 |

1226 | A particle is moved from (0,0) to ( (a, a) ) under a free force ( overrightarrow{boldsymbol{F}}=(3 hat{boldsymbol{i}}+4 hat{boldsymbol{j}}) ) from two paths, I is OP and path 2 is OQP. Let ( W_{1} ) and ( W_{2} ) be the work done by this force in these two paths. Then: A. ( W_{1}=W_{2} ) в. ( W_{1}, W_{2} ) c. ( W_{2}-2 W_{1} ) D. ( W_{2}-4 W_{1} ) | 11 |

1227 | A ball falls from a height of ( 5 m ) and strikes the roof of a lift. If at time of collision, lift is moving in the upward direction with a velocity of ( 1 mathrm{ms}^{-1} ). Then the velocity with which the ball rebounds after collision will be : A ( cdot 13 mathrm{ms}^{-1} ) upwards B. ( 12 mathrm{ms}^{-1} ) downwards C. ( 12 mathrm{ms}^{-1} ) upwards D. ( 11 mathrm{ms}^{-1} ) downwards | 11 |

1228 | A simple pendulum oscillates freely between points ( A ) and ( B ) We now put a peg (nail) at some point ( C ) as shown. As the pendulum moves from At to the right, the string will bend at ( C ) and the pendulum will go to its extreme point D. Ignoring friction, the point D. A. Will lie on the line AB B. Will lie above the line AB c. will lie below the line ( A B ) D. Will concide with B | 11 |

1229 | A body of mass ( 1 k g ) falls from a height of ( 5 m . ) How much energy does it possess at any instant? (Consider ( boldsymbol{g}= ) ( left.10 m s^{-2}right) ) A . ( 25 J ) в. ( 50 J ) c. 0 D. can not be determined with the help of given data | 11 |

1230 | What is the minimum energy required to lunch a satellite of mass ( m ) from the surface of a planet of mass ( M ) and radius ( R ) In a circular orbit at an altitude of ( 2 R ? ) A ( cdot frac{2 G m M}{3 R} ) в. ( frac{G m M}{2 R} ) c. ( frac{G m M}{3 R} ) D. ( frac{5 G m M}{6 R} ) | 11 |

1231 | 1. The displacement x in meter of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in second by the equation x = (1-3). The work done by the force (in joules) in first six seconds is a. 18m b. Zero c. 9m/2 d. 36m | 11 |

1232 | If ( hat{i}, hat{j} ) and ( widehat{k} ) are unit vectors along ( mathbf{x}, mathbf{y} ) and z axes respectively. the angle ( theta ) between the vector ( hat{mathbf{i}}+widehat{mathbf{j}}+widehat{boldsymbol{k}} ) and vector ( widehat{boldsymbol{i}} ) A ( cdot theta=cos ^{-1}left(frac{1}{sqrt{3}}right) ) В ( cdot theta=sin ^{-1}left(frac{1}{sqrt{3}}right) ) C ( cdot theta=cos ^{-1}left(frac{sqrt{3}}{2}right) ) D. ( theta=sin ^{-1}left(frac{sqrt{3}}{2}right) ) | 11 |

1233 | If ( g ) is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass ( boldsymbol{m} ) raised from the earth’s surface to a height equal to the radius ( R ) of the earth is ( ^{mathrm{A}} cdot frac{m g R}{4} ) в. ( frac{m g R}{2} ) ( mathbf{c} cdot m g R ) D. ( 2 m g R ) | 11 |

1234 | A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If ( e= ) coefficient of restitution, then what will be the ratio of velocity of two balls after collision? A ( frac{1-e}{1+e} ) в. ( frac{e-1}{e+1} ) c. ( frac{1+e}{1-e} ) D. ( frac{2+e}{e-1} ) | 11 |

1235 | A pair of bullocks exerts a force of ( 140 N ) on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field? | 11 |

1236 | Obtain the angle between ( vec{A}+vec{B} ) and ( vec{A}-vec{B} ) if ( vec{A}=2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}-2 hat{j} ) ( ^{A} cdot cos ^{-1}left(frac{4}{sqrt{65}}right) ) в. ( pi-cos ^{-1}left(frac{4}{sqrt{65}}right) ) ( ^{mathrm{c}} cdot sin ^{-1}left(frac{4}{sqrt{65}}right) ) D. ( -sin ^{-1}left(frac{4}{sqrt{65}}right) ) | 11 |

1237 | Find the ratio of speed of B with ( mathbf{A} ) ( left(i . e frac{V_{B}}{V_{A}}right) ) when all collisions end : ( A ) B. 2 ( c cdot 3 ) ( D ) | 11 |

1238 | Name the type of energy (kinetic energy ( boldsymbol{K} ) or potential energy ( boldsymbol{U} ) ) possessed in the following case. A piece of stone placed on the roof A. ( U ) в. ( K ) c. ( U ) and ( K ) D. No energy | 11 |

1239 | A body of mass ( 10 k g ) is moving with a velocity ( 20 m s^{-1} . ) If the mass of the body is doubled and its velocity is halved, find the ratio of the initia kinetic energy to the final kinetic energy. | 11 |

1240 | What is the velocity of centre of mass after the collision? ( A cdot vec{V}_{0} ) в. ( frac{vec{V}_{0}}{3} ) ( c cdot frac{vec{V}_{0}}{6} ) ( D ) | 11 |

1241 | A thin hollow sphere of mass ( m ) is completely filled with an ideal liquid of mass ( m . ) When sphere rolls with a velocity ( v, ) kinetic energy of the system is equal to: A ( cdot m v^{2} / 2 ) B. ( m v^{2} ) C. ( 4 m v^{2} / 3 ) D. ( 4 mathrm{mv}^{2} / 5 ) | 11 |

1242 | 36. During the displacement, which of the curves shown in the graph best represents the work done on the spring block system by the applied force? a. 1 b. 2 . c. 3 d. 4 | 11 |

1243 | A molecule in a gas container hits a horizontal wall with speed ( 200 mathrm{m} s^{-1} ) and angle ( 30^{0} ) with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic? | 11 |

1244 | 14. A 2144 kg freight car roles along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Fig. 8.308. Both springs are described by Hooke’s law with k, = 1600 Nm” and k, = 3400 Nm. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph in Fig. 8.309. The car comes to rest 50.0 cm after first contracting the two-spring system. Find the car’s initial speed (in x 10-Nm). common Fig. 8.308 Total force (N) 10 50 20 20 40 Distance (cm) Fig. 8.309 | 11 |

1245 | The vector ( hat{B}=4 hat{i}+2 hat{j}-S hat{k} ) is perpendicular to the vector ( overrightarrow{boldsymbol{A}}=mathbf{3} hat{mathbf{i}}+ ) ( hat{boldsymbol{j}}+boldsymbol{2} hat{boldsymbol{k}} ) if ( boldsymbol{S}= ) ( A ) B. 7 ( c cdot 6 ) D. 8 | 11 |

1246 | A ball is thrown from ground at an angle ( theta ) with horizontal and with an initial speed ( u_{0} . ) For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is ( V_{1} ) After hitting the ground, the ball rebounds at the same angle ( theta ) but with a reduced speed of ( u_{0} / alpha . ) Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is ( 0.8 V_{1}, ) the value of ( alpha ) is | 11 |

1247 | An overhead tank having some water possesses energy. A. Kinetic B. Potential c. Thermal D. Electrical | 11 |

1248 | 65. The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to tis a. Directly proportional to t b. Independent of t c. Directly proportional to t d. Directly proportional to t 1:1.. : 1. ADD 1. | 11 |

1249 | When a car of mass ( 1200 mathrm{kg} ) is moving with a velocity of ( 15 mathrm{ms}^{-1} ) on a rough horizontal road. Its engine is switched off. How far does the car travel before it comes to rest if the coefficient of kinetic friction between the road and tyres of the car is ( 0.5 ?left(g=10 m s^{-2}right) ) ( mathbf{A} cdot 6.2 m ) в. 20 ( m ) c. ( 22.5 m ) D. 30 | 11 |

1250 | A box of weight ( 150 k g f ) has gravitational potential energy stored in it equal to ( 14700 J ). Find the height of the box above the ground. (Take ( g= ) ( 9.8 N k g^{-1} ) ( mathbf{A} cdot 10 mathrm{cm} ) B. ( 10 k m ) ( c .1 m ) D. ( 10 m ) | 11 |

1251 | During inelastic collision of two particles. ( mathbf{A} cdot(K E)_{text {final }}=(K E)_{text {initial }} ) B. ( (K E)_{text {final }} ) must be greater than ( (K E)_{text {initial}} ) ( mathbf{C} cdot(K E)_{text {final}} ) must be less than ( (K E)_{text {initial}} ) D. ( (K E)_{text {final }} ) must be greater or less than ( (K E)_{text {initial }} ) | 11 |

1252 | Simple pendulum of length I has a maximum angular displacement ( theta ). The maximum kinetic energy of the bob is? A . ( m g mid(1-cos theta) ) B. ( 0.5 mathrm{mgl} ) c. ( mathrm{mg} ) D. 2mgl | 11 |

1253 | A uniform chain of length ( 2 m ) is kept on a table such that a length of ( 60 mathrm{cm} ) hangs freely from the edge of the table. The total mass of the chain is ( 4 k g ) What is the work done in pulling the entire chain on the table? A .125 ( J ) B. 3.6 J ( c .7 .25 ) D. ( 1200 J ) | 11 |

1254 | 27. A spring is compressed between two toy carts of masses m, and my. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same small time t. If the coefficients of friction u between the ground and the toy carts are equal, then the magnitude of displacements of the toy carts are in the ratio | 11 |

1255 | 17. The maximum positive displacement x is a. 273 m b. 2 m c. 4 m d. V2 m | 11 |

1256 | A ball of mass ( m ) moving with a speed ( 2 v_{0} ) collides head-on with an identical ball at rest. If ( e ) is the coefficient of restitution, then what will be the ratio of velocity of two balls after collision? A ( cdot frac{1-e}{1+e} ) в. ( frac{1+e}{1-e} ) c. ( frac{e-1}{e+1} ) D. ( frac{e+1}{e-1} ) | 11 |

1257 | Define coefficient of restitution. | 11 |

1258 | ( hat{text { i }} ) and ( hat{j} ) are unit vectors along along ( x ) and ( y- ) axis respectively. What is the magnitude and direction of the vectors ( hat{mathbf{i}}+hat{text { jand }} hat{boldsymbol{i}}-hat{boldsymbol{j}} ) ?What are the components of a vector ( A=2 hat{i}+3 hat{j} ) along the directions of ( hat{i}+hat{j} ) and ( hat{i}-hat{j} ) ? [You may use graphical method] | 11 |

1259 | A force ( overrightarrow{boldsymbol{F}}=(mathbf{5} hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}} 2 hat{boldsymbol{k}}) boldsymbol{N} quad ) is applied over a partivle which displaces it from its origin to the point ( vec{r}= ) ( (2 hat{i}-hat{j}) m . ) The work done on the particle in joules is then A . -7 B. +7 ( c cdot+10 ) D. +13 | 11 |

1260 | In a smooth stationary cart of length ( d ) a small block is projected along it’s length with velocity v towards front. Coefficient of restitution for each collision is e. The cart rests on a smooth ground and can move freely. The time taken by block to come to rest w,r.t cart is ( A ) B. ( frac{e d}{(l+e) v} ) ( c cdot d ) D. infinite | 11 |

1261 | A body moving at ( 2 mathrm{m} / mathrm{s} ) can be stopped over a distance ( x ). If its kinetic energy is doubled, how long will it go before coming to rest, retarding force remains unchanged? ( A ) B . ( 2 x ) c. ( 4 x ) D. ( 8 x ) | 11 |

1262 | Show that in case of one-dimensional elastic collision of two bodies, the relative velocity of separation after the collision is equal to the relative velocity of approach before the collision. | 11 |

1263 | A body having kinetic energy ( k ) moving on a rough horizontal surface is stopped at a distance ( x ) by constant frictional force. The force of friction exerted on the body is A ( cdot frac{k}{x} ) B. ( frac{sqrt{k}}{x} ) c. ( frac{k}{sqrt{x}} ) D. ( k x ) | 11 |

1264 | A car of mass 2000 kg changes its speed from ( 18 mathrm{km} / mathrm{h} ) to ( 90 mathrm{km} / mathrm{hr} ). Find the work done by the engine. | 11 |

1265 | A body of mass ‘m’ is raised from the surface of earth to a point which is at a height ( 5 R ) from the surface of the earth. The change in PE is A. ( 5 mathrm{mgR} ) в. ( frac{2 m g R}{3} ) c. ( frac{4}{5} m g r ) D. ( frac{5 m g R}{6} ) | 11 |

1266 | Consider two solid uniform spherical objects of the same density ( rho . ) One has radius ( R ) and the other has radius ( 2 R ) They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction? ( mathbf{A} cdot G pi^{2} R^{4} ) B. ( frac{128}{81} G pi^{2} R^{4} rho^{2} ) ( ^{mathbf{C}} cdot frac{128}{81} G pi^{2} ) ( stackrel{128}{87} G pi^{2} R^{2} ) | 11 |

1267 | A mass ( boldsymbol{m}=mathbf{1 4 k g} ) performing ( boldsymbol{S H} boldsymbol{M} ) as displacement, ( boldsymbol{x}=(mathbf{0 . 5 m}) sin (boldsymbol{6} boldsymbol{t}+boldsymbol{pi}) ) Determine maximum K.E. of the mass during its motion ( (text { in } boldsymbol{J}) ) A. ( frac{7 pi^{2}}{4} ) B . 49 c. 63 D. Data insufficient | 11 |

1268 | When a body is whirled in a circle, the work done on it is A. Positive B. Negative c. zero D. Infinite | 11 |

1269 | A planet whose mass and radius are both half of that of earth. Acceleration due to gravity(g) at its surface should be: A ( cdot 29.4 m / s e c^{2} ) в. ( 19.6 mathrm{m} / mathrm{sec}^{2} ) ( mathrm{c} cdot 9.8 mathrm{m} / mathrm{sec}^{2} ) D. ( 4.9 mathrm{m} / mathrm{sec}^{2} ) | 11 |

1270 | A car of mass ( 1000 mathrm{kg} ) moving with a speed ( 18 k m h^{-1} ) on a smooth road and colliding with a horizontally mounted spring of spring constnat ( 6.25 times ) ( 10^{3} N m^{-1} . ) The maximum compression of the spring is A . ( 1 m ) B. ( 2 m ) ( c .3 m ) D. ( 4 m ) | 11 |

1271 | A body of mass M was slowly hauled up a rough hill by a force ( F ) which at each point was directed along a tangent to the hill. Work done by the force. This question has multiple correct options A. Is independent of the shape of trajectory B. Depends upon the vertical component of displacemen but is independent of horizontal component c. Depends upon both the component D. Does not depend upon the coefficient of friction | 11 |

1272 | Potential energy increases with the increase in : A. work B. Force c. speed D. Position | 11 |

1273 | toppr Q Type your question ‘Igure. Ine coemcıent ( mu ) Is insurırcıent to start pure rolling. The sphere slides a length ( ell ) on the incline from rest and its kinetic energy becomes K. Then, the work done by friction will be A. ( -mu ) mglcos ( theta ) в. ( -m g ell sin theta+K ) ( c ) ( D ) | 11 |

1274 | The work done by a force ( overline{boldsymbol{F}}= ) ( left(-6 x^{3} iright) N ) in displacing particle from ( boldsymbol{x}=boldsymbol{a} boldsymbol{m} boldsymbol{t} boldsymbol{o} boldsymbol{x}=-boldsymbol{2} boldsymbol{m} ) is | 11 |

1275 | The work done on an object does not depends upon the: A. displacement B. force applied c. angle between force and displacement D. initial velocity of the object | 11 |

1276 | The potential energy function for a particle executing linear simple harmonic motion is given by ( V(x)=k x^{2} / 2, ) where ( k ) is the force constant of the oscillator. For ( boldsymbol{k}=mathbf{0 . 5} boldsymbol{N} boldsymbol{m}^{-1}, ) the ( operatorname{graph} ) of ( mathbf{V}(mathbf{x}) ) versus ( x ) is shown in Fig. Show that ( a ) particle of total energy 1 J moving under this potential must turn back when it reaches ( boldsymbol{x}=pm mathbf{2 m} ) | 11 |

1277 | 21. A bob of mass m is projected with a horizontal velocity V= 84 as shown in Fig. 8.224. In consequence, it moves V 2 in a circular path in a vertical plane by the inextensible string which passes over the smooth fixed peg. Find the maximum angle that the bob swings in the left hand side. Up V Fig. 8.224 | 11 |

1278 | Two bodies collide at the same temperature. Which of the following must remain conserved? (i) Velocity (ii) Momentum (iii) Kinetic energy A. Only (i) and (ii) B. Only (ii) c. only (i) and (iii) D. (i), (ii) and (iii) | 11 |

1279 | If the constant forces ( 2 hat{i}-5 hat{j}+6 hat{k} ) and ( -hat{mathbf{i}}+mathbf{2} hat{mathbf{j}}-hat{boldsymbol{k}} ) act on a particle due to which it is displaced from a point ( A(4,-3,-2) ) to a point ( B(6,1,-3) ) then the work done is A . 15 unit B. 9 unit c. -15 unit D. – 9 unit | 11 |

1280 | Choose the correct option: A. If only conservative forces act on a particle, the kinetic energy remains constant. B. If the net force acting on an object is zero, then the object is at rest. C. If net mechanical work is done on a body, the body must accelerate. D. If net mechanical work is done on a body, the speed of body remains unchanged. | 11 |

1281 | If a particle of ( 1 K g ) at mars is pushed through a distance of ( 5 m ). Calculate the total work done. ( left(operatorname{given} mu_{m}=0.3 ) and right. ( left.boldsymbol{g}_{m}=mathbf{5} boldsymbol{m} / boldsymbol{s}^{2}right) ) A . ( 10 J ) в. 7.5 .5 ( c .0 J ) D. None | 11 |

1282 | A body of mass ( 1 k g ) is made to trave with a uniform acceleration of ( 30 mathrm{cm} / mathrm{s}^{2} ) over a distance of ( 2 mathrm{m} ), the work done is: ( mathbf{A} cdot 6 J ) в. ( 60 J ) ( c .0 .6 . J ) D. 0.3 .5 | 11 |

1283 | Two satellites of earth, ( S_{1} ) and ( S_{2} ), are moving in the same orbit. The mass of ( S_{1} ) is four times the mass of ( S_{2} ). Which one of the following statements is true? A. The kinetic energies of the two satellites are equal B. The time period of ( S_{1} ) is four times that of ( S_{2} ) c. The potential energies of earth and satellite in the two cases are equal D. ( S_{1} ) and ( S_{2} ) are moving with the same speed | 11 |

1284 | If the vector ( 6 hat{i}-3 hat{j}-6 hat{k} ) is decomposed into vectors parallel and perpendicular to the vector ( hat{i}+hat{j}+hat{k} ) then the vectors are A ( .-(hat{i}+hat{j}+hat{k}) & 7 hat{i}-2 hat{j}-5 hat{k} ) B. ( -2(hat{i}+hat{j}+hat{k}) & 8 hat{i}-hat{j}-4 hat{k} ) ( mathbf{c} cdot+2(hat{i}+hat{j}+hat{k}) & 8 hat{i}-hat{j}-4 hat{k} ) D. none | 11 |

1285 | a. 8a b. 24a c. 160 d. Zero 72. In the position shown in Fig. 8.251, the spring is at its natural length. The block of mass m is given a velocity Vo towards the vertical support at t = 0. The coefficient of friction between the block and the surface is given by u = Ox, where a is a positive constant and x is the position of the block from its starting position. The block comes to rest for the first time at x, which is VO Fig. 8.251 m b. Vo Vk + amg m vonas d. None of these 1 . c. | 11 |

1286 | Statement 1:If ( vec{A} cdot vec{B}=vec{B} cdot vec{C} ) then ( vec{A} ) may not always be equal to ( overrightarrow{boldsymbol{C}} ) Statement 2: The dot product of two vector involves cosine of the angle between the two vectors. A. a) Statement- – is false, Statement- 2 is true B. b) Statement-1 is true, Statement-2 is true, Statement 2 is a correct explanation for statement- c. c) Statement- – is true, Statement-2 is true; Statement 2 is not a correct explanation for statement- D. d) Statement-1 is true, Statement-2 is false | 11 |

1287 | An object of mass ( 1 mathrm{kg} ) has a PE of 1 relative to the ground when it is at a height of: A. ( 0.102 mathrm{m} ) B. ( 1 mathrm{m} ) c. ( 9.8 mathrm{m} ) D. 32 ( m ) | 11 |

1288 | Given ( k_{1}=1500 N m^{-1}, k_{2}= ) ( mathbf{5 0 0} N boldsymbol{m}^{-1}, boldsymbol{m}_{1}=mathbf{2 k g}, boldsymbol{m}_{2}=mathbf{1 k g} . ) Find: a. Potential energy stored in the springs in equilibrium, and b. work done in slowly pulling down ( m_{2} ) by ( 8 mathrm{cm} ) | 11 |

1289 | When a rubber-bank is stretched by a distance ( x, ) it exerts a restoring force of magnitude ( F=a x+b x^{2} ) where ( a ) and ( b ) are constants. The work done in stretching the unstretched rubber band by ( boldsymbol{L} ) is: ( ^{mathrm{A}} cdot frac{a L^{2}}{2}+frac{b L^{3}}{3} ) ( ^{mathrm{B}} cdot frac{1}{2}left(frac{a L^{2}}{2}+frac{b L^{3}}{3}right) ) ( mathbf{c} cdot a L^{2}+b L^{3} ) D. ( frac{1}{2}left(a L^{2}+b L^{3}right) ) | 11 |

1290 | A bird flying in the sky has A. K.E. only B. P.E. only C. Neither K.E. nor P.E. D. Both K.E. and P.E. | 11 |

1291 | A ball is dropped from height hon the ground level. If the coefficient of restitution is e then the height upto which the ball will go after ( n^{t h} ) jump will be- ( A cdot frac{h}{e^{2 n}} ) B. ( frac{e^{2 n}}{h} ) ( mathbf{c} cdot h e^{n} ) D. ( h e^{2 n} ) | 11 |

1292 | A boy weighing ( 25 k g f ) climbs up from the first floor at height ( 3 m ) above the ground to the third floor at height ( 9 m ) above the ground. What will be the increase in the gravitational potential energy? Consider ( boldsymbol{g}=10 m s^{-2} ) ( mathbf{A} cdot 1 k J ) B. ( 1.3 k J ) c. ( 1.5 k J ) D. None of these | 11 |

1293 | ( Q ) туре уочт question rod. The rod can revolve in a vertical plane around the point A. What horizontal velocity must be imparted to the end of the rod ( C ) to deflect it to the horizontal position? (Given acceleration due to gravity ( =g ) 4. ( sqrt{2 g} ) ( 3 cdot sqrt{2 cdot 4 g} ) ( c cdot sqrt{3 g} ) ( -sqrt{3.60} ) 0 | 11 |

1294 | If ( vec{A} cdot vec{B}=0, ) the angle between the vectors ( A ) and ( B ) will be: A ( cdot 0^{circ} ) B. ( 60^{circ} ) ( c cdot 90^{circ} ) ( D cdot 180^{circ} ) | 11 |

1295 | A tunnel is dug along a diameter of the earth. If ( M_{e} ) and ( R_{e} ) are the mass and radius, respectively, of the earth, then the force on a particle of mass ( m ) placed in the tunnel at a distance ( r ) from the centre is : ( ^{mathbf{A}} cdot frac{G M_{e} m}{R_{e}^{3}} r ) в. ( frac{G M_{e} m}{R_{s}^{3} r} ) c. ( frac{G M_{e} m R_{e}^{3}}{r} ) ( ^{mathrm{D}} cdot frac{G M_{e} m}{R^{2}} ) | 11 |

1296 | Value of v for which particle hit vertical walls ( n ) times is ( left(x n+frac{5}{2}right) mathrm{m} / mathrm{s} ) and finally hit the point ( A ) which is the centre point between the two vertical walls (all collison are elastic) Find ( x ) ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) ) | 11 |

1297 | The vector ( vec{A}=vec{i}+vec{j} ) where ( vec{i}, vec{j} ) are unit vectors along ( X ) and ( Y ) axes respectively makes an angle of with ( X ) axis. ( A cdot 0^{circ} ) B. ( 45^{circ} ) ( c cdot 60 ) D. ( 90^{circ} ) | 11 |

1298 | A man of mass ( 60 k g ) climbs up a ( 20 m ) long staircase on the top of a building 10 ( m ) high. What is the work done by him? ( left(text { Takeg }=10 m s^{-2}right) ) A. ( 12 k J ) J 5 J. 12 . в. ( 6 k J ) c. ( 3 k J ) D. ( 18 k J ) | 11 |

1299 | A particle is projected vertically upwards from the surface of the earth(radius R) with a kinetic energy equal to half of the minimum value needed for it to escape. Find the height to which it rises above the surface of earth. | 11 |

1300 | A body of mass 5 kg falls from a height of ( 10 m ) to 4 m. Calculate the loss in potential energy of the body. (Take ( g= ) ( left.10 m s^{-2}right) ) A . ( 0 . J ) в. ( 300000 J ) c. ( 3 J ) D. ( 300 J ) | 11 |

1301 | Two charges ( +5 mu C ) and ( -5 mu C ) separated by ( 4 m m ) form an electric dipole. The dipole is placed in a uniform electric field of ( 4 times 10^{5} N / C . ) The work done in rotating the electric dipole through ( 180^{circ}, ) if it starts from the positions of ( boldsymbol{theta}=mathbf{0} ) is A. ( 4 m J ) в. ( 8 m J ) c. ( 12 m J ) D. ( 16 m J ) | 11 |

1302 | A bullet of mass ( m=50 ) gm strikes a bag of mass ( mathrm{M}=5 mathrm{kg} ) hanging from a fixed point, with a horizontal velocity ( bar{V}_{p} . ) If bullet sticks to the sand bag then just after collision the ratio of final ( & ) initial kinetic energy of the bullet is approximately: A ( cdot 10^{-2} ) – ( ^{-2} ) B. ( 10^{-3} ) ( mathbf{c} cdot 10^{-6} ) D. ( 10^{-4} ) | 11 |

1303 | Velocity of a particle of mass ( 2 mathrm{kg} ) changes from ( overrightarrow{boldsymbol{v}}_{1}=-2 widehat{boldsymbol{i}}-widehat{boldsymbol{2}} hat{boldsymbol{j}} boldsymbol{m} / boldsymbol{s} ) to ( overrightarrow{boldsymbol{v}}_{2}=(widehat{boldsymbol{i}}-widehat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} ) after colliding with a plane surface This question has multiple correct options A. the angle made by the plane surface with the positive ( x ) -axis is ( 90^{circ}+tan ^{-1}left(frac{1}{3}right) ) B. the angle made by the plane surface with the positive x-axis is ( tan ^{-1}left(frac{1}{3}right) ) C. the direction of change in momentum makes an angle ( tan ^{-1}left(frac{1}{3}right) ) with the positive ( x ) -axis. D. the direction of the change in momentum makes an angle ( 90^{circ}+tan ^{-1}left(frac{1}{3}right) ) with the plane surface. | 11 |

1304 | A projectile is launched vertically upward. It explodes into two pieces at the top point of its trajectory. One piece has twice the mass of the other. Immediately after the explosion, the more massive piece has kinetic energy ( boldsymbol{E} ). What is the total kinetic energy of both pieces immediately after the explosion? ( mathbf{A} cdot 1.5 E ) B. ( 2 E ) ( c .3 E ) D. not enough information to answer E. Answer required | 11 |

1305 | If ( vec{A}=a hat{i}+2 hat{j}-5 hat{k}, vec{B}=2 hat{i}-hat{j}-4 hat{k} ) are perpendicular to each other, the value of ( boldsymbol{a} ) is: ( A cdot 9 ) B. -9 ( c cdot 4 ) ( D cdot-4 ) | 11 |

1306 | 16. In Fig. 8.220, the light spring is of force constant k and is on a smooth horizontal surface. Initially the spring is relaxed. Calculate the work done by an external agent to lower the hanging body of mass M slowly, till it remains in equilibrium. 00000 От Fig. 8.220 | 11 |

1307 | The average transnational KE of N2 molecules at NTP is- ( mathbf{A} cdot 0.15 J ) в. 0.036 .5 c. ( 0.032 J ) D. ( 152 J ) | 11 |

1308 | ( vec{A}, vec{B} ) and ( vec{C} ) satisfy the relations, ( vec{A} cdot vec{B}=0 ) and ( vec{A} cdot vec{C}=0, ) then ( vec{A} ) is parallel to A . ( vec{B} ) в. ( vec{c} ) c. ( vec{B} times vec{C} ) D. 高广 | 11 |

1309 | A child pulls a toy bus through a distance of ( 8 mathrm{m} ) on a smooth horizontal floor. The string held in the child’s hand makes an angle of ( 60^{circ} ) with the horizontal surface. If the force applied by the child is 3 N. Calculate the work done by the child in pulling the toy car. | 11 |

1310 | A steel ball strikes a fixed smooth steel plate placed on a horizontal surface at an angle ( theta ) with the vertical. If the coefficient of restitution is ( e ), the angle at which the rebound will take place is ( A cdot theta ) B. ( tan ^{-1}left[frac{tan theta}{e}right] ) ( c cdot e tan theta ) D. ( tan ^{-1}left[frac{e}{tan theta}right] ) | 11 |

1311 | In a one-dimensional collision between two particles, their relative velocity is ( overrightarrow{v_{1}} ) before the collision and ( overrightarrow{v_{2}} ) after collision: A. ( overrightarrow{v_{1}}=overrightarrow{v_{2}} ) if the collision is elastic B. ( overrightarrow{v_{1}}=-overrightarrow{v_{2}} ) if the collision is elastic c. ( |overrightarrow{v_{2}}|=|overrightarrow{v_{1}}| ) in all cases D. ( overrightarrow{v_{1}}=-k overrightarrow{v_{2}} ) in all cases, where ( k geq 1 ) | 11 |

1312 | 5. A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its ve- locity as it reaches a position where the string is horizontal (IIT JEE, 1998) a. Su² – 28L b. √2qL d. /2cu² – 8L) is c. Su² – gl | 11 |

1313 | Mass of a planet is ( 5 times 10^{24} mathrm{kg} ) and radius is ( 6.1 times 10^{6} mathrm{m} . ) The energy needed to send a 2 kg body into space from its surface, would be. A. 9 joule B. 18 joule C. ( 2.2 times 10^{8} ) joule D. ( 1.1 times 10^{8} ) joul | 11 |

1314 | Force acting on a particle moving in a straight line varies with the velocities of the particle as ( boldsymbol{F}=boldsymbol{K} . boldsymbol{V} . ) Where ( boldsymbol{K} ) is constant. The work done by this force in time ( t ) is A . ( K V t ) B. ( K^{2} V^{2} t^{2} ) c. ( K^{2} V t ) D. ( K V^{2} t ) | 11 |

1315 | The track shown in figure is frictionless. The block B of mass ( m ) is pushed along the track with some speed. The collision between ( A ) and ( B ) is perfectly elastic. With what velocity should the block ( A ) be started to get the sleeping man awakened ? | 11 |

1316 | 10. An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60%, what is the power of the engine? Take g =10 ms. a. 33 kW b. 3.3 kW c. 0.33 kW d. 0.033 kW | 11 |

1317 | A ball drops from a ceiling of a room, and after rebounding twice from the floor reaches a height equal to half that of the ceiling. Show that coefficient of restitution is ( sqrt[4]{frac{1}{2}} ) | 11 |

1318 | Equal net forces act on two different blocks ( A ) and ( B ) of masses ( m ) and ( 4 m ) respectively. For same displacement, identify the correct statement. A ‘ their kinetic energies are in the ratio ( frac{K_{A}}{K_{B}}=frac{1}{4} ) B. Their speeds are in the ratio ( frac{v_{A}}{v_{B}}=frac{1}{1} ) c. work done on the blocks are in the ratio ( frac{W_{A}}{W_{B}}=frac{1}{1} ) D. All of the above | 11 |

1319 | The kinetic energy acquired by a mass ( mathrm{m} ) after travelling a fixed distance from rest under the action of constant force is A. directly proportional to ( sqrt{m} ) B. directly proportional to c. independent of ( m ) D. directly proportional to ( frac{1}{sqrt{m}} ) | 11 |

1320 | With what speed must a ball be thrown down for it to bounce 10 m higher | 11 |

1321 | Fig. 8. 6. AB is a quarter of smooth circular track of radius R=6m A particle P of mass 0.5 kg moves along the track from A to B under the action of the following forces. B Fig. 8.210 a. A force Fı directed always towards the point B; its magnitude is constant and is equal to 20 N. b. A force F2 directed along the instantaneous tangent to the circular track; its magnitude is (15 – 105) N, where S is the distance travelled in metre. C. A horizontal force of magnitude 30 N. Find the work done by forces mentioned in (a), (b) and (c) | 11 |

1322 | A meter stick of mass 400 g is pivoted at one end and displaced through an angle ( 60^{0} . ) The increase in its potential energy is | 11 |

1323 | Two wires if same material and area if cross section but with length in the ratio 5: 3 are streached by the same force. The ratio of work done in two cases is A . 5: 8 B. 8: 5 ( c .5: 3 ) D. 3: 5 | 11 |

1324 | A solid iron ball A of radius ( r ) collids head on with another stationary solid iron ball ( B ) of radius ( 2 r . ) The ratio of their speeds just after the collision ( (e=0.5) ) is: A . 3 B. 4 ( c cdot 2 ) D. | 11 |

1325 | A rope ladder with a length ( l ) carrying a man with a mass ( m ) at its end is attached to the basket of a balloon with a mass ( M . ) The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height ( h ). The change in potential energy of the man is: A ( . m g l ) в. ( M g(l-h) ) ( c cdot 1 / 2 m g l ) D. ( m g(l-h) ) | 11 |

1326 | A bullet of mass 10 g moving with velocity of ( 100 mathrm{m} / mathrm{sec} ) hits a wooden log and penetrates it up to thickness of 5 ( mathrm{cm} . ) The resistance force of log is: A . 200 B. 500 N c. ( 1000 N ) D. 600 N | 11 |

1327 | Find the maximum extension in the spring A ( cdot frac{1}{4} v_{0} sqrt{frac{m}{5 k}} ) В ( cdot frac{3}{4} v_{0} sqrt{frac{m}{5 k}} ) ( ^{mathbf{c}} cdot frac{1}{3} v_{0} sqrt{frac{m}{5 k}} ) D. ( quad frac{1}{8} v_{0} sqrt{frac{m}{5 k}} ) | 11 |

1328 | Two point masses 1 and 2 move with uniform velocities ( boldsymbol{v}_{1} ) and ( boldsymbol{v}_{2} ) respectively. Their initial position vectors are ( r_{1} ) and ( r_{2}, ) respectively. Which of the following should be satisfied for the collision of the point masses? A ( cdot frac{r_{1}-r_{2}}{left|r_{2}-r_{1}right|}=frac{v_{1}-v_{2}}{left|v_{2}-v_{1}right|} ) В. ( frac{r_{2}-r_{1}}{left|r_{1}-r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}-v_{1}right|} ) c. ( frac{r_{2}-r_{1}}{left|r_{2}+r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}+v_{1}right|} ) D. ( frac{r_{2}+r_{1}}{left|r_{2}+r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}+v_{1}right|} ) | 11 |

1329 | 48. A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in Fig. 8.240. Initially, the spring is in the natural length state. Then the maximum positive work that the applied force F can do is (given that string does not break) Fig. 8.240 I a. F² b. 25² c. c. oo d. F | 11 |

1330 | 3. A bob of mass m, suspended by a string of length 1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length 12, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob. after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio 11/l, is (JEE Advanced, 2013) | 11 |

1331 | Assertion In a two-body collision, the momenta of the particles are equal and opposite to one another, before as well as after the collision when measured in the centre of mass frame. Reason The momentum of the system is zero from the centre of mass frame. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

1332 | Consider the following facts about energy. I. The electrical energy can be stored in a capacitor to be recovered on its discharge. Il. It is stored in the electromagnetic radiations in electric and magnetic fields. III. In a closed system, the total energy is variable. IV. Potential energy is stored in a body when it changes its configuration. ( A cdot ) ।, III and ( 1 V ) B. I, II and IV C. I, II and III D. II, III and IV | 11 |

1333 | A neutron travelling with a velocity ( v ) and kinetic energy E collides perfectly elastically head on with the nucleus of an atom of mass number ( A ) at rest. The fraction of total energy retained by the neutron is: ( ^{A} cdotleft(frac{A-1}{A+1}right)^{2} ) ( ^{text {B. }}left(frac{A+1}{A-1}right)^{2} ) ( ^{c}left(frac{A-1}{A}right)^{2} ) ( ^{mathrm{D}}left(frac{A+1}{A}right)^{2} ) | 11 |

1334 | A man raises a box of mass ( 50 k g ) to a height of ( 2 m ) in 2 minutes, while another man raises the same box to the same height in 5 minutes. Compare the work done by them. A . 1: 1 B . 2: 1 c. 1: 2 D. 4: 1 | 11 |

1335 | A ( 3000 mathrm{Kg} ) meteorite has a speed of ( 300 m s^{-1} ) just before colliding head on with the energy that is the recoil speed of the earth? Mass of the earth ( =6 times ) ( 10^{24} K g ) | 11 |

1336 | An object of mass ( m ) sliding along a frictionless surface collides with the stationary object of mass ( m ). The two bodies stick together. If the kinetic energy of the two-body system is ( boldsymbol{E} ) Calculate the initial velocity of the first object before impact? A ( cdot sqrt{E / 2 m} ) B. ( sqrt{2 E / 2 m} ) c. ( sqrt{2 E / m} ) D. ( sqrt{E / m} ) E ( .2 sqrt{E / m} ) | 11 |

1337 | A bullet of mass ( m ) is being fired from a stationary gun of mass ( M . ) If the velocity of the bullet is ( v, ) the velocity of the gun is A ( cdot frac{M v}{m+M} ) B. ( frac{m v}{M} ) c. ( frac{(M+m) v}{M} ) D. ( frac{M+m}{M v} ) | 11 |

1338 | Consider a gravity- free hall in which an experimenter of mass ( 50 mathrm{kg} ) is resting on a ( 5 k g ) pillow, ( 8 f t ) above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of ( 8 f t / s ) The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter’s head. Find the time elapsed in the process. | 11 |

1339 | A ball falls from a height of ( 10 mathrm{m} ) on to a horizontal plane. if the coefficient 0 restitution is 0.6. the height to which it rebounds after 2 collision is approximate. ( mathbf{A} cdot 2.24 m ) B. ( 0.47 m ) ( mathrm{c} .0 .3 mathrm{m} ) D. ( 1.296 mathrm{m} ) | 11 |

1340 | A body of mass ( 3 mathrm{kg} ) collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body? ( A cdot 1 mathrm{kg} ) B. 2.5 ( mathrm{kg} ) ( c cdot 2 k g ) ( D .5 mathrm{kg} ) | 11 |

1341 | A body of mass ( 3 mathrm{kg} ) is under a force, which causes a displacement in it given by ( S=frac{t^{3}}{3}left(text { in }^{prime} m^{prime}right) . ) Find the work done by the force in first 2 seconds. | 11 |

1342 | An ideal spring with spring constant ( k ) is hung from the ceiling and a block of mass ( M ) is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (Given acceleration due to gravity ( =g) ) A ( cdot frac{4 M g}{k} ) в. ( frac{2 M g}{k} ) c. ( frac{M g}{k} ) D. ( frac{M g}{2 k} ) | 11 |

1343 | A particle is projected at ( 60^{00} ) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is- ( A cdot K ) B. zero ( c cdot k / 4 ) D. K /2 | 11 |

1344 | The coefficient of restitution e for a perfectly inelastic collision is: ( mathbf{A} cdot mathbf{1} ) B. ( c cdot alpha ) ( D ) | 11 |

1345 | A body of mass 5 kg rests on a rough horizontal surface of friction coefficient 0.2. The is pulled through a distance 10 ( mathrm{m} ) by a horizontal force of ( 25 N . ) The kinetic energy acquired by it is A . ( 200 J ) в. ( 150 J ) ( c cdot 100 J ) D. ( 50 J ) | 11 |

1346 | A ball of mass m approaches a wall of ( operatorname{mass} M(>>m) ) with the speed ( 4 mathrm{m} / mathrm{s} ) along normal to the wall. The speed of wall is ( 1 mathrm{m} / mathrm{s} ) towards the ball. The speed of the ball after an elastic collision with the wall is- A. ( 5 mathrm{m} / mathrm{s} ) away from the wall B. 3 m/s away from the wall c. ( 9 mathrm{m} / mathrm{s} ) away from the wall D. ( 6 mathrm{m} / mathrm{s} ) away from the wall | 11 |

1347 | 3. Two blocks A and B, each of mass m, are connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in Fig. 8.314. A third identical block C, also of mass m moves on the floor with a speed v along the line joining A and B and collides with A, then L Fig. 8.314 (IIT JEE, 1993) a. The KE of the AB system at maximum compression of the spring is zero. b. The KE of the AB system at maximum compression of the spring is (1/4)mv. c. The maximum compression of the spring is v. m d. The maximum compression of the spring is V2k Descanina Tune | 11 |

1348 | A massive ball moving with a speed ( boldsymbol{v} ) collide with a tiny ball having a very small mass, immediately after the impact the second ball will move at speed approximately equal to : ( A cdot infty ) B. ( frac{v}{2} ) ( c ) D. ( 2 v ) | 11 |

1349 | The co-efficient of restitution for a perfectly elastic collision is: A . B. 0 c. lies in between 0 and 1 D. infinity | 11 |

1350 | A spring of force constant ( 800 mathrm{N} / mathrm{m} ) has an extension of ( 5 mathrm{cm} ). Find work done in extending it from ( 5 mathrm{cm} ) to ( 15 mathrm{cm} ) | 11 |

1351 | A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is ( A cdot h e^{2 n} ) В. ( h e^{n} ) c. ( frac{2^{e n}}{h} ) D. ( frac{h}{2^{e n}} ) | 11 |

1352 | Set the angles made by following vectors with ( x ) -axis in increasing order: a) ( 3 hat{i}+4 hat{j} ) b) ( 4 hat{i}+3 hat{j} ) c) ( hat{boldsymbol{i}}+hat{boldsymbol{j}} ) ( A cdot a, b, c ) B. ( c, b, a ) ( c cdot b, c, a ) D. a, c, b | 11 |

1353 | Consider the situation shown if figure Initially the string is unstretched when the system is released from rest Assuming no friction in the pulley, what is the maximum elongation of the | 11 |

1354 | The type of collision is: A . perfectly elastic B. elastic C . inelastic D. perfectly inelastic | 11 |

1355 | ( operatorname{Let} vec{A}=hat{i} A cos theta+hat{j} A sin theta, ) be any vector. Another vector ( vec{B} ) which is normal to ( vec{A} ) is : A ( . hat{i} B cos theta+hat{j} B sin theta ) B. i ( B ) sin ( theta+hat{j} B cos theta ) c. ( hat{i} B sin theta-hat{j} B cos theta ) D. ( hat{i} B cos theta-hat{j} B sin theta ) | 11 |

1356 | If both the objects have the same PE curve as shown in the figure, then A . For objects having total energy ( E_{2} ), all values of r are possible B. For the object having total energy ( E_{2} ), values of ( r<r_{0} ) are only possible C. For the object having total energy ( E_{1} ), all values of rare possible D. None of the above | 11 |

1357 | A block of mass ( mathrm{m} ) is kept over another block of mass ( 2 mathrm{m} ) and the system rests on a smooth horizontal surface. The coefficient of friction between the blocks is ( 0.50 . ) Find the work done by the force of friction on the smaller block by the bigger block during a displacement d the system, when a force mg is applied to the lower block. ( mathbf{A} cdot frac{m g d}{3} ) B. mgd c. ( frac{m F d}{2(M+m)} ) D. Zero | 11 |

1358 | As a builder lifts a ( 3.0 mathrm{kg} ) brick at a steady speed from the ground to a platform 2.0 meters high. How much work is done on the brick by the builder and by the earth while it is being lifted, and what is the net work done on the brick by all forces while it is being lifted? A. ( 60 mathrm{N},-60 mathrm{N}, mathrm{O} ) в. – -60 N, 60 N, 0 c. ( 60 mathrm{N}, 60 mathrm{N}, 0 ) D. – -60 N,-60 N, 0 E. 60 N, 60 N, -60 N | 11 |

1359 | One of the two forces is double and the other resultant is equal to the greater force. The angle between then is ( mathbf{A} cdot cos ^{-1}(1 / 2) ) B . ( cos ^{-1}(-1 / 2) ) c. ( cos ^{-1}(1 / 4) ) D. ( cos ^{-1}(-1 / 4) ) | 11 |

1360 | If vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k}, ) then the value of ( alpha ) is : A . -1 в. ( frac{1}{2} ) ( c cdot-frac{1}{2} ) D. | 11 |

1361 | 2. Two masses of 1 g and 4 g are moving with equal ki energies. The ratio of the magnitudes of their momenta is (IIT JEE, 1980) a. 4:1 b. √2:1 c. 1:2 d. 1:16 | 11 |

1362 | Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of ( 3 m s^{-1} ) and ( 2 m s^{-1} ) respectively. They collide with each other. After collision, glass sphere of mass 10 g moves with a velocity of ( 2.5 m s^{-1} . ) Find the velocity of the second ball after collision. A ( .2 .25 m s^{-1} ) B. ( 5.5 m s^{-1} ) ( mathbf{c} cdot 2.75 m s^{-1} ) D. ( 7.5 m s^{-1} ) | 11 |

1363 | A uniform rod of mass ( m ) and length ( l ) is resting on a smooth horizontal surface. A particle of mass ( m / 2 ) travelling with a speed ( v_{0} ) hits the rod normally and elastically. Then, This question has multiple correct options A ( cdot ) final velocity of the particle is ( -frac{2}{15} v_{0} ) B. final velocity of the particle is ( -frac{1}{15} v_{0} ) c. angular velocity of the rod ( frac{8 v_{0}}{5 e} ) D. angular velocity of the rod ( frac{6 v_{0}}{5 ell} ) | 11 |

1364 | Ball A of mass m, after sliding from an inclined plane, strikes elastically another ball B of same mass at rest. Find the minimum height h so that ball B just completes the circular motion of the surface at C. (All surfaces are smooth.) Fig. 8.268 b. h = 2R a. h=2R d. h = 3R | 11 |

1365 | A body of weight 1 newton has a potential energy of 1 joule relative to the ground when it is at a height of: A . ( 1 mathrm{m} ) B. 9.8 m ( mathrm{c} cdot 1 / 9.8 mathrm{m} ) D. o m | 11 |

1366 | Potential energy is classified into which two energy? A. Gravitational and Elastic Potential Energy B. Kinetic and Elastic Potential Energy c. Mechanical and Elastic Potential Energy D. None | 11 |

1367 | The gravitational potential energy of a body is ( _{-}–_{-}-_{-}- ) to its height above the surface of the Earth. A. directly proportional B. indirectly proportional c. independent D. none | 11 |

1368 | A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic energy, ( boldsymbol{E}_{mathbf{0}} ). The minimum energy of explosion will be ( mathbf{A} cdot 6 E_{0} ) в. ( frac{4 E_{0}}{3} ) c. ( 4 E_{0} ) D. ( 8 E_{0} ) | 11 |

1369 | Consider the following statements A) Linear momentum of a system of particles is zero B) Kinetic energy of a system of particles is zero Then A. A does not imply B & B does not imply A B. A implies B and B does not imply A c. A does not imply B but B implies A D. A implies B and B implies A | 11 |

1370 | A block of mass 2 kg slides on a rough surface at ( t=0, ) if speed is ( 2 mathrm{m} / mathrm{s} ). It stops after covering a distance of ( 20 mathrm{cm} ) because of friction. Find work done by the friction. | 11 |

1371 | Energy required to accelerate a car from ( 10 m s^{-1} ) to ( 20 m s^{-1} ) compared with that required to acceleration it from 0 to ( 10 m s^{-1} ) is ( A ). twice B. three times c. four times D. same | 11 |

1372 | A wound-up watch spring possesses A. kinetic energy B. elastic potential energy c. nuclear energy D. sound energy | 11 |

1373 | Tlus ration 8.35 A plate of mass m, length b, and breadth a is initially lying on a horizontal floor with length parallel to the floor and breadth perpendicular to the floor. Find the work done to erect it on its breadth. BOLA Fig. 8.74 | 11 |

1374 | 33. In the above question, the average power delivered by gravity is a. -mg u cos a b. -mgu sina c. mgucosa d. mgu sina | 11 |

1375 | If the kinetic energy of a body increases b ( 4 % ) the momentum: A. increases by 2% B. increases by 4% c. increases by ( 8 % ) D. increases by 16% | 11 |

1376 | Find the speed of ( C ) after collision of ( B ) and ( C ) for first time. A ( cdot frac{V}{4} ) в. ( frac{2 V}{4} ) c. ( frac{3 V}{4} ) ( D ) | 11 |

1377 | A truck weighing 1000 kgf changes its speed from ( 36 k m h^{-1} ) to ( 72 k m h^{-1} ) in 2 minutes. ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) . ) Calculate the work done by the engine A ( cdot 1.5 times 10^{4} J ) В. ( 1 times 10^{5} J ) c. ( 7.2 times 10^{5} J ) D. ( 0 . J ) | 11 |

1378 | Find the fraction of kinetic energy lost when the body of mass ( M ) is jerked into motion A ( cdot frac{M}{M+m} ) В. ( frac{M}{M-m} ) c. ( frac{2 M}{M+m} ) D. ( frac{M}{2(M+m)} ) | 11 |

1379 | A simple pendulum is vibrating with an angular amplitude of ( frac{r}{2} . ) The value of ( alpha ) for which the resultant acceleration has a direction along the horizontal is : ( mathbf{A} ) ( frac{pi}{2} ) B. ( 180^{circ} ) c. ( cos ^{-1}left(frac{1}{sqrt{3}}right) ) D. ( cos ^{-1}left(frac{1}{sqrt{2}}right) ) | 11 |

1380 | At which depth, we get the necessary temperature for OTEC in the ocean? ( A cdot O m ) to ( 20 m ) B. 100 m to 300 m c. ( 400 mathrm{m} ) to ( 600 mathrm{m} ) D. 700 ( mathrm{m} ) to ( 900 mathrm{m} ) | 11 |

1381 | A cricket ball of mass 250 g collides with a bat with velocity ( 10 mathrm{m} / mathrm{s} ) and returns with the same velocity within 0.01 second. The force acted on bat is: A. 25 B. 50 N c. 250 N D. 500 N | 11 |

1382 | The potential energy function associated with the force ( overrightarrow{boldsymbol{F}}=mathbf{4 x y} hat{mathbf{i}}+ ) ( 2 x^{2} hat{j} ) is A ( cdot U=-x^{2} y ) B . ( U=-2 x^{2} y+ ) constant C. ( U=2 x^{2} y+ ) constant D. Not defined | 11 |

1383 | A constant force ( boldsymbol{F}=(hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}}) boldsymbol{N} ) acts on a particle and displace it from ( (-1 m, 2 m, 1 m) ) to ( (2 m,-3 m, 1 m) ) Then the work done by the force is: ( mathbf{A} cdot 12 J ) в. ( -10 J ) c. ( -12 J ) D. ( 15 J ) | 11 |

1384 | An object with mass ( 2 mathrm{kg} ) moves with a velocity of ( 10 mathrm{m} / mathrm{s} ). What is the net force on the body? A. 20 B. on ( c cdot 5 N ) D. 25 N | 11 |

1385 | In Fig. Force ( F ) is gradually increased from zero. Draw the graph between applied force ( F ) and tension ( T ) in the string. The coefficient of static friction between the block and the ground is ( mu_{s} ) | 11 |

1386 | A stone is tied to the middle of a string and suspended from one end as shown in the figure. Here ( mathrm{S} ) is the stone and 0 is the pint of suspension (ii) if we increase the pull at ( mathrm{P} ) gradually, the string will break A. Below the stone B. At the point P itself c. Above the stone D. Nothing can be decided | 11 |

1387 | A boy pulls a ( 5 k g ) block along a ( 20 m ) long horizontal surface at a constant velocity by applying a horizontal force ( boldsymbol{F} ) If the coefficient of kinetic friction is 0.2 how much work does the boy do on the block? ( left(g=10 m s^{-2}right) ) ( mathbf{A} cdot 100 J ) B. ( 300 J ) c. ( 200 J ) D. ( 400 J ) | 11 |

1388 | What is the angular velocity of rotation of this rigid body? A ( cdot frac{V_{0}}{5 d} ) B. ( frac{V_{0}}{d} ) c. ( frac{V_{0}}{3 d} ) D. | 11 |

1389 | A weight of ( 5 mathrm{N} ) is moved upon a frictionless inclined plane from ( R ) to ( Q ) as shown. What is the work done in joule? A ( cdot 15 ) B. 20 ( c cdot 25 ) D. 35 | 11 |

1390 | Compute the work which must be performed (in ( K g f-m ) ) to slowly pump water out of a hemispherical reservoir of radius ( boldsymbol{R}=mathbf{0 . 6 m} ) | 11 |

1391 | The work done by the tension T in the above process is A . ( Z ) ero B . ( T(L-L cos theta) ) c. ( -T L ) D. ( -T L sin theta ) | 11 |

1392 | A man has a strange ability to jump from any height to another with ease. The manjumps to P then to Q, R, S, T and then into water. For which jump will he require the highest energy? A. Land to P в. s to ( T ) ( c cdot Q ) to ( R ) D. R to | 11 |

1393 | Which of the following quantity is different from others? A. work B. Kinetic energy c. Force D. Potential energy | 11 |

1394 | A girl in a swing is ( 2.5 m ) above ground at the maximum height and at ( 1.5 m ) above the ground at the lowest point. Her maximum velocity in the swing is ( left(g=10 m s^{-2}right) ) В. ( 2 sqrt{5} mathrm{ms}^{-1} ) D. ( 3 sqrt{2} mathrm{ms}^{-1} ) E ( cdot 4 sqrt{2} m s^{-1} ) | 11 |

1395 | A spring is kept compressed by a toy car of mass ( 150 g . ) On releasing the car it moves with a speed of ( 0.2 m s^{-1} . ) So, the elastic potential energy of the spring is ( A .3 m J ) B. ( 3 J ) c. ( 1.5 m J ) D. ( 4 m J ) | 11 |

1396 | A force acts on a ( 3 g ) particle in such a way that the position of the particle as a function of time is given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}- ) ( 4 t^{2}+t^{3}, ) where ( x ) is in meters and ( t ) is in second. The work done during the first 4 second is: A. ( 490 m J ) J в. ( 450 m J ) ( mathrm{c} .528 mathrm{mJ} ) D. ( 530 m J ) | 11 |

1397 | 5. Find average power transferred to the body in first 2 s. a. 50W b. 100 W c. 150 W d. 200 W To Problems 68 | 11 |

1398 | Assertion In an inelastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason In an elastic collision, the linear momentum of the system is conserved. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

1399 | A block of mass ( m ) has initial velocity ( u ) having direction ( +x ) axis. The block stops after covering distance ( S ) causing an extension in the spring of spring constant ( K ) holding it. If ( mu ) is the kinetic friction between the block and the surface on which it was moving, the distances ( boldsymbol{S} ) is : A ( cdot frac{1}{K} mu^{2} m^{2} g^{2} ) B. ( frac{1}{K}left(m K u^{2}-mu^{2} m^{2} g^{2}right)^{frac{1}{2}} ) c. ( frac{1}{K}(sqrt{mu^{2} m^{2} g^{2}+m K u^{2}}-mu m g) ) D ( cdot frac{1}{K}left(mu^{2} m^{2} g^{2}-m K u^{2}+mu m gright)^{frac{1}{2}} ) | 11 |

1400 | When a body moves in a circular path, no work is done by the force since: A. force and displacement are perpendicular to each other. B. the force is always away from the centre. C. there is no displacement. D. there is no net force. | 11 |

1401 | If the potential energy of two molecules is given by, ( U=frac{A}{r^{12}}-frac{B}{r^{6}} ) then at equilibrium position, its potential energy is equal to: A ( cdot frac{A^{2}}{4 B} ) B. ( -frac{B^{2}}{4 A} ) c. ( frac{2 B}{A} ) D. 3A | 11 |

1402 | A spring block system is placed on a horizontal surface so as to just fit within two vertical walls. The spring is initially unstretched. The coefficient of restitution for collison is ( e=frac{1}{2} . ) The block is pulled to the left by a distance ( x=1 c m ) and released from rest. The time between second and third collision of the block with the wall is A ( cdot 2 pi sqrt{frac{m}{k}} ) В. ( pi sqrt{frac{m}{k}} ) c. ( frac{pi}{2} sqrt{frac{m}{k}} ) D. ( frac{pi}{4} sqrt{frac{m}{k}} ) | 11 |

1403 | A bullet of mass ( A ) and velocity ( B ) is fired into a block of wood of mass ( C . ) If loss of any mass and friction be neglected, the velocity of the system will be ( ^{text {A }} cdot frac{A B}{A+C} ) в. ( frac{A+C}{B+C} ) c. ( frac{A C}{B+C} ) D. ( frac{A+B}{A C} ) | 11 |

1404 | A electron at rest is accelerated by applying a ( P . D . ) of ( 250 mathrm{V} ). What is its ( K . E . ) in electron volt ? A ( .250 e V ) B. 225 eV c. 200 eV D. 150 eV | 11 |

1405 | Two identical ( 5 mathrm{kg} ) blocks are moving with same speed of ( 2 m s^{-1} ) towards each other along a frictionless horizontal surface. The two blocks collide, stick together, and come to rest. Consider the two blocks as a system The work done by external and internal forces are respectively, ( A cdot 0,0 ) B. 0, 20J c. 0,-20 D. 20J, -20J | 11 |

1406 | ilustration 8.15 An inclined plane is moving up with constant velocity v. A block pt on incline is at rest. Calculate the work Mone by gravity, friction force, and normal reaction on block in time interval of Fig. 8.28 | 11 |

1407 | A force of 5 N acts on a 15 kg particle initially at rest. What will be instantaneous power due to the force at the end of ( 6^{t h} ) second. A. 10 watt B. 5 watt c. 20 watt D. 25 watt | 11 |

1408 | 8. Select the correct option(s). a. A single external force acting on a particle necessarily changes its momentum and kinetic energy. b. A single external force acting on a particle necessarily changes its momentum. c. The work-energy theorem is valid for all types of forces: internal, external, conservative as well as non- conservative. d. The kinetic energy of the system can be increased without applying any external force on the system. | 11 |

1409 | When a body slides down from an inclined plane, Work is said to be done because of gravity. State whether given statement is True/ False? A. True B. False | 11 |

1410 | Give an example for each of the following energy conversion: (1) electrical energy to kinetic energy. chemical energy to electrical energy (3) sound energy to electrical energy | 11 |

1411 | Two bodies of equal weights are kept at heights ( h ) and 1.5 respectively. The ratio of their potential energy is A .3: 2 B. 1: 1 ( c cdot 2: 3 ) D. 3: 4 | 11 |

1412 | When ( 1 g ) of water ( operatorname{at} 0^{circ} C ) and ( 1 times ) ( 10^{5} N / m^{2} ) pressure is converted into ice of volume ( 1.091 mathrm{cm}^{3} ), the external work done will be: A. 0.0091 joule B. 0.0182 joule c. -0.0091 joule D. – 0.0182 joule | 11 |

1413 | For the system shown in the figure, the cylinder on the left at L has a mass of ( 600 mathrm{kg} ) and a cross sectional area of ( 800 c m^{2}, ) the piston on the right, at ( S ) has cross sectional area ( 25 c m^{2} ) and negligible weight. If the appartus is filled with oil. ( left(rho=0.75 g m / c m^{3}right) ) Find the force ( F ) requird to hold the system in equilibrium. A . 50 N В. 33 n D. 22.5 | 11 |

1414 | An object of mass ( mathrm{m} ) is allowed to fall from rest along a rough inclined plane. The speed of the object on reaching the bottom of the plane is proportional to? ( mathbf{A} cdot m^{0} ) B. ( m ) ( c cdot m^{2} ) D. ( m^{-1} ) | 11 |

1415 | i.e., potom estration 8.37 A conservative force held function is given hy F = k/r’, where k is a constant. Determine the potential energy function U(r) assuming zero potential energy at r= ro. h. Also, determine the potential energy at r=o. | 11 |

1416 | What is the recoil velocity of the gun of mass ( 8 mathrm{kg} ) when a bullet of mass ( 10 mathrm{g} ) is fired from it with a velocity of ( 400 mathrm{m} / mathrm{s} ? ) ( mathbf{A} cdot 5 mathrm{m} / mathrm{s} ) B. ( 2 mathrm{m} / mathrm{s} ) c. ( 50 mathrm{m} / mathrm{s} ) D. ( 0.5 mathrm{m} / mathrm{s} ) | 11 |

1417 | A wedge of mass ( M ) is kept at rest on smooth surface, a particle of mass ( boldsymbol{m} ) hits the wedge normally. Find the velocity of wedge and particle just after collision. Take coefficient of restitution as ( e ) | 11 |

1418 | A proton in motion makes head on collision with an unknown particle at rest. If the collision is perfectly elastic and proton rebounds back with ( frac{4}{9} ) of its initial kinetic energy after collision, the mass of unknown particle is A. Equal to mass of proton B. Twice the mass of proton c. 3 times the mass of proton D. 5 times the mass of proton | 11 |

1419 | A particle of mass ( m_{1} ) moving with a velocity of ( 5 m / s ) collides head on with a stationary particle of mass ( m_{2} . ) After collision both the particle move with a common velocity of ( 4 m / s, ) then the value ( boldsymbol{m}_{1} / boldsymbol{m}_{2} ) is: A .4: B. 2: ( c cdot 1: 8 ) D. 1: | 11 |

1420 | A rod of length 1 m and mass 0.5 kg hinged at one end, is initially hanging vertical. The other end is now raised slowly until it makes an angle ( 60^{circ} ) with the vertical. The required work is (use ( left.boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) ) A ( cdot frac{5}{2} J ) в. ( frac{5}{4} J ) c. ( |