Tiêu đề 07. Work, Energy and Power Easy.pdf ✅

1. A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is r mv 2 and is directed towards the center. What is the work done by this force in moving the body over half the circumference of the circle (a) 2 2 r mv  (b) Zero (c) 2 2 r mv (d) 2 2 mv r 2. If the unit of force and length each be increased by four times, then the unit of energy is increased by (a) 16 times (b) 8 times (c) 2 times (d) 4 times 3. A man pushes a wall and fails to displace it. He does (a) Negative work (b) Positive but not maximum work (c) No work at all (d) Maximum work 4. The same retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance will be (a) The same (b) Doubled (c) Halved (d) Four times 5. A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is (a) 0° (b) 30° (c) 60° (d) 90° 6. You lift a heavy book from the floor of the room and keep it in the book-shelf having a height 2 m. In this process you take 5 seconds. The work done by you will depend upon (a) Mass of the book and time taken (b) Weight of the book and height of the book-shelf (c) Height of the book-shelf and time taken (d) Mass of the book, height of the book-shelf and time taken 7. A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them are in the ratio (a) 1 : 2 (b) 1 : 1 (c) 2 : 1 (d) 4 : 1 8. A force ) ˆ 3 ˆ F = (5i + j newton is applied over a particle which displaces it from its origin to the point ) ˆ 1 ˆ r = (2i − j metres. The work done on the particle is (a) – 7 joules (b) + 13 joules (c) + 7 joules (d) + 11 joules 9. A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by 2 3 x = 3t − 4t + t , where x is in metres and t is in seconds. The work done during the first 4 seconds is (a) 5.28 J (b) 450 mJ (c) 490 mJ (d) 530 mJ 10. A body of mass 10 kg is dropped to the ground from a height of 10 metres. The work done by the gravitational force is ( 9.8 / sec ) 2 g = m (a) – 490 Joules (b) + 490 Joules (c) – 980 Joules (d) + 980 Joules 11. Which of the following is a scalar quantity (a) Displacement (b) Electric field (c) Acceleration (d) Work 12. The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of 15° with the horizontal is (a) 4.36 kJ (b) 5.17 kJ (c) 8.91 kJ (d) 9.82 kJ 13. A force F i j k ˆ 4 ˆ 6 ˆ = 5 + −  acting on a body, produces a displacement s 6i 5k.    = + Work done by the force is (a) 18 units (b) 15 units (c) 12 units (d) 10 units 14. A force of 5 N acts on a 15 kg body initially at rest. The work done by the force during the first second of motion of the body is (a) 5 J (b) J 6 5 (c) 6 J (d) 75 J 15. A force of 5 N, making an angle  with the horizontal, acting on an object displaces it by 0.4m along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force is (a) 1.5 N (b) 2.5 N (c) 3.5 N (d) 4.5 N 16. The work done against gravity in taking 10 kg mass at 1m height in 1sec will be (a) 49 J (b) 98 J (c) 196 J (d) None of these 17. The energy which an − e acquires when accelerated through a potential difference of 1 volt is called (a) 1 Joule (b) 1 Electron volt
(c) 1 Erg (d) 1 Watt. 18. A body of mass 6kg is under a force which causes displacement in it given by 4 2 t S = metres where t is time. The work done by the force in 2 seconds is (a) 12 J (b) 9 J (c) 6 J (d) 3 J 19. A body of mass 10kg at rest is acted upon simultaneously by two forces 4 N and 3N at right angles to each other. The kinetic energy of the body at the end of 10 sec is (a) 100 J (b) 300 J (c) 50 J (d) 125 J 20. A cylinder of mass 10kg is sliding on a plane with an initial velocity of 10m/s. If coefficient of friction between surface and cylinder is 0.5, then before stopping it will describe (a) 12.5 m (b) 5 m (c) 7.5 m (d) 10 m 21. A force of ) ˆ 4 ˆ (3 i + j Newton acts on a body and displaces it by ) . ˆ 4 ˆ (3 i + j m The work done by the force is (a) 10 J (b) 12 J (c) 16 J (d) 25 J 22. A 50kg man with 20kg load on his head climbs up 20 steps of 0.25m height each. The work done in climbing is (a) 5 J (b) 350 J (c) 100 J (d) 3430 J 23. A force F i j k ˆ 3 ˆ 2 ˆ = 6 + − acts on a particle and produces a displacement of . ˆ ˆ 3 ˆ s = 2i − j + xk If the work done is zero, the value of x is (a) – 2 (b) 1/2 (c) 6 (d) 2 24. A particle moves from position r i j k ˆ 6 ˆ 2 ˆ 1 =3 + −  to position r i j k ˆ 9 ˆ 13 ˆ 2 = 14 + +  under the action of force . ˆ 3 ˆ ˆ 4i + j + k N The work done will be (a) 100 J (b) 50 J (c) 200 J (d) 75 J 25. A force F i cj k ˆ 2 ˆ ˆ ( ) = 3 + +  acting on a particle causes a displacement: s i j k ˆ 3 ˆ 2 ˆ ( )= −4 + +  in its own direction. If the work done is 6 J, then the value of 'c' is (a) 0 (b) 1 (c) 6 (d) 12 26. In an explosion a body breaks up into two pieces of unequal masses. In this (a) Both parts will have numerically equal momentum (b) Lighter part will have more momentum (c) Heavier part will have more momentum (d) Both parts will have equal kinetic energy 27. Which of the following is a unit of energy (a) Unit (b) Watt (c) Horse Power (d) None 28. If force and displacement of particle in direction of force are doubled. Work would be (a) Double (b) 4 times (c) Half (d) 4 1 times 29. A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of o 60 with the x-axis and displaces it along the x-axis by 4 metres. The work done by the force is (a) 2.5 J (b) 7.25 J (c) 40 J (d) 20 J 30. A force ) ˆ 4 ˆ F = (5i + j N acts on a body and produces a displacement ) ˆ 3 ˆ 5 ˆ S = (6i − j + k m. The work done will be (a) 10 J (b) 20 J (c) 30 J (d) 40 J 31. A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table (a) 7.2 J (b) 3.6 J (c) 120 J (d) 1200 J 32. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that (a) Its velocity is constant (b)Its acceleration is constant (c) Its kinetic energy is constant (d)It moves in a straight line 33. A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is (a) Zero (b) mv J (c) m/v.J (d) v/m J 34. A force F i j k)N ˆ 2 ˆ 3 ˆ = (5 + +  is applied over a particle which displaces it from its origin to the point r = (2 ˆ i − ˆ j)m  . The work done on the particle in joules is (a) – 7 (b) +7 (c) +10 (d) +13
35. The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to (a) 0 m (b) m (c) 2 m (d) m 36. If a force F i j ˆ 5 ˆ = 4 +  causes a displacement s i k ˆ 6 ˆ = 3 +  , work done is (a) 4  6 unit (b) 6  3 unit (c) 5 6 unit (d) 4  3 unit 37. A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him (a) Zero (b) Positive (c) Negative (d) Nothing can be said 38. It is easier to draw up a wooden block along an inclined plane than to haul it vertically, principally because (a) The friction is reduced (b) The mass becomes smaller (c) Only a part of the weight has to be overcome (d) ‘g’ becomes smaller 39. Two bodies of masses 1 kg and 5 kg are dropped gently from the top of a tower. At a point 20 cm from the ground, both the bodies will have the same (a) Momentum (b) Kinetic energy (c) Velocity (d) Total energy 40. Due to a force of (6 ˆ i + 2 ˆ j)N the displacement of a body is (3 ˆ i − ˆ j)m , then the work done is (a) 16 J (b) 12 J (c) 8 J (d) Zero 41. A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is (a) 1 : 2 : 3 (b) 1 : 4 : 9 (c) 1 : 3 : 5 (d) 1 : 5 : 3 42. A particle moves under the effect of a force F = Cx from x = 0 to 1 x = x . The work done in the process is (a) 2 Cx1 (b) 2 1 2 1 Cx (c) Cx1 (d) Zero 43. A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration 4 g . Work done by the cord on the block is (a) 4 d Mg (b) 4 3 d Mg (c) 4 3 d − Mg (d) Mgd 44. Two springs have their force constant as 1 k and ( ) 2 1 2 k k  k . When they are stretched by the same force (a) No work is done in case of both the springs (b) Equal work is done in case of both the springs (c) More work is done in case of second spring (d) More work is done in case of first spring 45. A spring of force constant 10 N/m has an initial stretch 0.20 m. In changing the stretch to 0.25 m, the increase in potential energy is about (a) 0.1 joule (b) 0.2 joule (c) 0.3 joule (d) 0.5 joule 46. The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be (a) 30 (b) 40 (c) 10 (d) 20 47. Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio (a) 4 : 1 (b) 1 : 4 (c) 2 : 1 (d) 1 : 2 48. A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is (a) 84 J (b) 68 J (c) 23 J (d) 8 J 49. A position dependent force F x x newton 2 = 7 − 2 + 3 acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m . The work done in joules is (a) 70 (b) 270 (c) 35 (d) 135 50. A body of mass 3 kg is under a force, which causes a displacement in it is given by 3 3 t S = (in m). Find the work done by the force in first 2 seconds (a) 2 J (b) 3.8 J (c) 5.2 J (d) 24 J 51. The force constant of a wire is k and that of another wire is 2k. When both the wires are stretched through same distance, then the work done
(a) 2 W2 = 2W1 (b) W2 = 2W1 (c) W2 = W1 (d) 2 5 1 W = 0. W 52. A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is (a) 0.01m (b) 0.1m (c) 0.2m (d) 0.5m 53. When a 1.0kg mass hangs attached to a spring of length 50 cm, the spring stretches by 2 cm. The mass is pulled down until the length of the spring becomes 60 cm. What is the amount of elastic energy stored in the spring in this condition, if g = 10 m/s2 (a) 1.5 Joule (b) 2.0 Joule (c) 2.5 Joule (d) 3.0 Joule 54. A spring of force constant 800 N/m has an extension of 5cm. The work done in extending it from 5cm to 15 cm is (a) 16 J (b) 8 J (c) 32 J (d) 24 J 55. When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by (a) 100 J (b) 200 J (c) 300 J (d) 400 J 56. A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to (a) 4 J (b) 54 J (c) 415 J (d) None 57. A spring of spring constant 5  103 N/m is stretched initially by 5cm from the unstretched position. Then the work required to stretch it further by another 5cm is (a) 6.25 N-m (b) 12.50 N-m (c) 18.75 N-m (d) 25.00 N-m 58. A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N / m . The maximum compression of the spring would be (a) 0.15 m (b) 0.12 m (c) 1.5 m (d) 0.5 m 59. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to (a) 2 x (b) x e (c) x (d) x e log 60. A spring with spring constant k when stretched through 1 cm, the potential energy is U. If it is stretched by 4 cm. The potential energy will be (a) 4U (b) 8U (c) 16 U (d) 2U 61. A spring with spring constant k is extended from x = 0 to 1 x = x . The work done will be (a) 2 1 kx (b) 2 1 2 1 kx (c) 2 2 1 kx (d) 1 2kx 62. If a long spring is stretched by 0.02 m, its potential energy is U. If the spring is stretched by 0.1 m, then its potential energy will be (a) 5 U (b) U (c) 5U (d) 25U 63. Natural length of a spring is 60 cm, and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced in the spring is, (Take 2 g = 9.8 m / s ) (a) 4.9 cm (b) 0.49 cm (c) 9.4 cm (d) 0.94 cm 64. The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant) (a) k T 2 2 (b) 2 2 2k T (c) 2 2 T k (d) k T 2 2 65. The potential energy of a body is given by, U = 2 A − Bx (Where x is the displacement). The magnitude of force acting on the particle is (a) Constant (b) Proportional to x (c) Proportional to 2 x (d) Inversely proportional to x 66. The potential energy between two atoms in a molecule is given by 12 6 ( ) x b x a U x = − ; where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when (a) 6 5 11 b a x = (b) 6 2b a x = (c) x = 0 (d) 6 2 b a x = 67. Which one of the following is not a conservative force