Title 07. Work, Energy Power hard.pdf ✅

1. Two masses of 1g and 9g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is (a) 1 : 9 (b) 9 : 1 (c) 1 : 3 (d) 3 : 1 2. A body of mass 2 kg is thrown upward with an energy 490 J. The height at which its kinetic energy would become half of its initial kinetic energy will be [ 2 g = 9.8 m / s ] (a) 35 m (b) 25 m (c) 12.5 m (d) 10 m 3. A 300 g mass has a velocity of ) ˆ 4 ˆ (3i + j m/sec at a certain instant. What is its kinetic energy (a) 1.35 J (b) 2.4 J (c) 3.75 J (d) 7.35 J 4. A particle moves in a potential region given by 8 4 400 2 U = x − x + J. Its state of equilibrium will be (a) x = 25m (b) x = 0.25 m (c) x = 0.025 m (d) x = 2.5 m 5. A long spring is stretched by 2 cm, its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be (a) U / 25 (b) U / 5 (c) 5 U (d) 25 U 6. A spring of spring constant 5 10 N / m 3  is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is (a) 6.25 N-m (b) 12.50 N-m (c) 18.75 N-m (d) 25.00 N-m 7. 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 8. A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length x. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case (a) x (b) 2x (c) 3x (d) x/2 9. Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is (a) 2 2 1 kx (b) 2 2 1 − kx (c) 2 4 1 kx (d) 2 4 1 − kx 10. A proton has a positive charge. If two protons are brought near to one another, the potential energy of the system will (a) Increase (b) Decrease (c) Remain the same (d) Equal to the kinetic energy 11. A rod of mass m and length l is lying on a horizontal table. The work done in making it stand on one end will be (a) mgl (b) 2 mgl (c) 4 mgl (d) 2mgl 12. A metre stick, of mass 400 g, is pivoted at one end displaced through an angle o 60 . The increase in its potential energy i (a) 1 J (b) 10 J (c) 100 J (d) 1000 J 13. Once a choice is made regarding zero potential energy reference state, the changes in potential energy (a) Are same (b) Are different (c) Depend strictly on the choice of the zero of potential energy (d) Become indeterminate 14. A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is (a) MgL (b) 3 MgL (c) 9 MgL (d) 18 MgL 15. A chain is placed on a frictionless table with one fourth of it hanging over the edge. If the length of the chain is 2m and its mass is 4kg, the energy need to be spent to pull it back to the table is (a) 32 J (b) 16 J (c) 10 J (d) 2.5 J 16. A uniform chain of length 2m is held on a smooth horizontal table so that half of it hangs over the edge. If it is released from rest, the velocity with which it leaves the table will be nearest to (a) 2 m/s (b) 4 m/s (c) 6 m/s (d) 8 m/s 17. Two stones each of mass 5kg fall on a wheel from a height of 10m. The wheel stirs 2kg water. The rise in temperature of water would be (a) 2.60 C (b) 1.20 C (c) 0.320 C (d) 0.120 C 18. A boy is sitting on a swing at a maximum height of 5m above the ground. When the swing passes through the mean position which is 2m above the ground its velocity is approximately (a) 7.6 m/s (b) 9.8 m/s (c) 6.26 m/s (d) None 60o
19. A block of mass M slides along the sides of a bowl as shown in the figure. The walls of the bowl are frictionless and the base has coefficient of friction 0.2. If the block is released from the top of the side, which is 1.5 m high, where will the block come to rest ? Given that the length of the base is 15 m (a) 1 m from P (b) Mid point (c) 2 m from P (d) At Q 20. A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external resistive force ‘R’. When the velocity of the car is ‘v’, the rate at which the engine of the car is doing work will be (a) Rv (b) mav (c) (R + ma)v (d) (ma − R)v 21. 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 (a) v (b) 2 v (c) 3 v (d) 4 v 22. A pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, power of the motor has to be increased to (a) 16 times (b) 4 times (c) 8 times (d) 2 times 23. A force applied by an engine of a train of mass kg 6 2.05 10 changes its velocity from 5 m/s to 25 m/s in 5 minutes. The power of the engine is (a) 1.025 MW (b) 2.05 MW (c) 5MW (d) 5 MW 24. From a water fall, water is falling at the rate of 100 kg/s on the blades of turbine. If the height of the fall is 100m then the power delivered to the turbine is approximately equal to (a) 100Kw (b) 10 kW (c) 1Kw (d) 1000 Kw 25. A particle moves with a velocity ˆ 1 6 ˆ 3 ˆ 5 − v = i − j + k ms  under the influence of a constant force . ˆ 20 ˆ 10 ˆ F = 10i + j + k N  The instantaneous power applied to the particle is (a) 200 J-s –1 (b) 40 J-s –1 (c) 140 J-s –1 (d) 170 J-s –1 26. A car of mass 1250 kg experience a resistance of 750 N when it moves at 30ms–1 . If the engine can develop 30kW at this speed, the maximum acceleration that the engine can produce is (a) 2 0.8 − ms (b) 2 0.2 − ms (c) 1 0.4 − ms (d) 2 0.5 − ms 27. A bus weighing 100 quintals moves on a rough road with a constant speed of 72km/h. The friction of the road is 9% of its weight and that of air is 1% of its weight. What is the power of the engine. Take g = 10m/s2 (a) 50 Kw (b) 100 Kw (c) 150 kW (d) 200 Kw 28. Two men with weights in the ratio 5 : 3 run up a staircase in times in the ratio 11 : 9. The ratio of power of first to that of second is (a) 11 15 (b) 15 11 (c) 9 11 (d) 11 9 29. A dam is situated at a height of 550 metre above sea level and supplies water to a power house which is at a height of 50 metre above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were 80% efficient is (a) 8 MW (b) 10 MW (c) 12.5 MW (d) 16 MW 30. A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as (a) 2 P  t (b) P  t (c) P  t (d) 3 / 2 P  t 31. n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be (a) mnu (b) 2 mnu (c) 4 mnu (d) mnu 2 1 32. A particle of mass m moving with horizontal speed 6 m/sec. If m<velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are (a) – V and 2V (b) 2V and – V (c) V and – 2V (d) – 2V and V 35. A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball attains velocity u and big ball v. Then what is the value of v (a) u M m M m + − (b) u M m m + (c) u M m m + 2 (d) u M m M + 36. A car of mass 400kg and travelling at 72 kmph crashes into a truck of mass 4000 kg and travelling at 9 kmph, in the same direction. The car bounces back at a speed of 18 kmph. The speed of the truck after the impact is (a) 9 kmph (b) 18 kmph (c) 27 kmph (d) 36 kmph 37. A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is (a) m 2uM (b) M 2um (c) M m u 1 + 2 (d) m M u 1 + 2 38. A ball moving horizontally with speed v strikes the bob of a simple pendulum at rest. The mass of the bob is equal to that of the ball. If the collision is elastic the bob will rise to a height (a) g v 2 (b) g v 2 2 (c) g v 4 2 (d) g v 8 2 39. A moving body with a mass m1 strikes a stationary body of mass m2. The masses m1 and m 2 should be in the ratio 2 1 m m so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact. Then the ratio 2 1 m m is (a) 1/ 25 (b) 1/5 (c) 5 (d) 25 40. Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide with the row of 6 balls from left. What will happen (a) One ball from the right rolls out with a speed 2v and the remaining balls will remain at rest (b) Two balls from the right roll out with speed v each and the remaining balls will remain stationary (c) All the six balls in the row will roll out with speed v/6 each and the two colliding balls will come to rest (d) The colliding balls will come to rest and no ball rolls out from right 41. A moving mass of 8 kg collides elastically with a stationary mass of 2 kg. If E be the initial kinetic energy of the mass, the kinetic energy left with it after collision will be (a) 0.80 E (b) 0.64 E (c) 0.36 E (d) 0.08 E 42. A neutron travelling with a velocity v and K.E. 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 neutron is (a) 2 1 1       + − A A (b) 2 1 1       − + A A (c) 2 1       − A A (d) 2 1       + A A 43. A neutron with 0.6MeV kinetic energy directly collides with a stationary carbon nucleus (mass number 12). The kinetic energy of carbon nucleus after the collision is (a) 1.7 MeV (b) 0.17 MeV (c) 17 MeV (d) Zero 44. A body of mass m moving along a straight line collides with a body of mass nm which is also moving with a velocity kv in the same direction. If the first body comes to rest after the collision, then the velocity of second body after the collision would be (a) (1 nk ) nv + (b) (1 nk ) nv − (c) n (1 − nk )v (d) n (1 + nk )v 45. A ball moving with velocity of 9m / s collides with another similar stationary ball. After the collision both the balls move in directions making an angle of o 30 with the initial direction. After the collision their speed will be (a) 2.6m / s (b) 5.2m / s (c) 0.52m / s (d) 52m / s 46. A ball of mass 1kg , moving with a velocity of 0.4m / s collides with another stationary ball. After the collision, the first ball moves with a velocity of 0.3m / s in a direction making an angle of o 90 with its initial direction. The momentum of second ball after collision will be (in kg-m/s) (a) 0.1 (b) 0.3 (c) 0.5 (d) 0.7 47. Keeping the principle of conservation of momentum in mind which of the following collision diagram is not correct (a) (b) M1   M2 M M2 1 M1   M2 M M2 1 v →
(c) (d) 48. Three particles A, B and C of equal mass are moving with the same velocity v along the medians of an equilateral triangle. These particle collide at the centre G of triangle. After collision A becomes stationary, B retraces its path with velocity v then the magnitude and direction of velocity of C will be (a) v and opposite to B (b) v and in the direction of A (c) v and in the direction of C (d) v and in the direction of B 49. A ball B1 of mass M moving northwards with velocity v collides elastically with another ball B2 of same mass but moving eastwards with the same velocity v. Which of the following statements will be true (a) B1 comes to rest but B2 moves with velocity 2v (b) B1 moves with velocity 2v but B2 comes to rest (c) Both move with velocity v / 2 in north east direction (d) B1 moves eastwards and B2 moves north wards 50. A body of mass 40kg having velocity 4m / s collides with another body of mass 60kg having velocity 2m / s . If the collision is inelastic, then loss in kinetic energy will be (a) 440 J (b) 392 J (c) 48 J (d) 144 J 51. One sphere collides with another sphere of same mass at rest inelastically. If the value of coefficient of restitution is 2 1 , the ratio of their speeds after collision shall be (a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1 52. The ratio of masses of two balls is 2 : 1 and before collision the ratio of their velocities is 1 : 2 in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If e = (5/6), the ratio of speed of each ball before and after collision would be (a) (5/6) times (b) Equal (c) Not related (d) Double for the first ball and half for the second ball 53. Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and come to rest after impact. The coefficient of restitution is (a) 3 2 (b) 3 1 (c) 6 1 (d) 2 3 54. Two cars of same mass are moving with same speed v on two different roads inclined at an angle  with each other, as shown in the figure. At the junction of these roads the two cars collide inelastically and move simultaneously with the same speed. The speed of these cars would be (a) 2 cos  v (b) cos 2 v (c) 2 cos 2 v  (d) 2v cos  55. Which of the following is not a perfectly inelastic collision (a) Striking of two glass balls (b) A bullet striking a bag of sand (c) An electron captured by a proton (d) A man jumping onto a moving cart 56. A metal ball of mass 2kg moving with a velocity of 36km / h has an head-on collision with a stationary ball of mass 3kg . If after the collision, the two balls move together, the loss in kinetic energy due to collision is (a) 40 J (b) 60 J (c) 100 J (d) 140 J 57. A mass of 20kg moving with a speed of 10m / 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 (a) 600 J (b) 800 J (c) 1000 J (d) 1200 J 58. A neutron having mass of 1.67 × 10 −27kg and moving at 10 8m/s collides with a deutron at rest and sticks to it. If the mass of the deutron is 3.34 × 10 −27kg; the speed of the combination is (a)2.56 × 10 3m/s (b)2.98 × 10 5m/s (c)3.33 × 10 7m/s (d)5.01 × 10 9m/s 59. A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v . The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity (a) v / 2 (b) 2v (c) v / 2 (d) v 60. A particle of mass ' m' moving with velocity ' v' collides in elastically with a stationary particle of mass '2m' . The speed of the system after collision will be m m  v v v v v B C A M1 90o M M2 M1 2 M1 90o  M2 M1 M2