Title 07. Work, Energy and Power Med.pdf ✅

1. A raindrop of mass 1 g falling from a height of 1 km hits the ground with a speed of 1 50ms − . If the resistive force is proportional to the speed of the drop, then the work done by the resistive force is : (Take 2 1 − g = ms ) (a) 10 J (b) -10 J (c) 8.75 J (d) -8.75 J 2. An object of mass m is released from the top of a smooth inclined plane of height h. Its speed at the bottom of the plane is proportional to : (a) 0 m (b) m (c) 2 m (d) 1 m − 3. A body is being raised to a height h from the surface of earth. What is the sign of work done by : (i) Applied force (ii) Gravitational force? (a) Positive, Positive. (b) Positive, Negative (c) Negative, Positive (d) Negative, Negative 4. The angle between force k) ˆ j 5 ˆ i 4 ˆ F = (3 + −  unit and displacement k) ˆ j 3 ˆ i 4 ˆ d = (5 + +  unit is : (a) cos (0.16) −1 (b) cos (0.32) −1 (c) cos (0.24) −1 (d) cos (0.64) −1 5. A body constrained to move along y-axis is subjected to a constant force F = − ˆ i + 2 ˆ j+ 3k ˆ N  . The work done by this force in moving the body a distance of 4 m along y-axis is : (a) 4 J (b) 8 J (c) 12 J (d) 24 J 6. In the question number 11, the work done against force of friction is : (a) 8.7 J (b) 10.7 J (c) 7.8 J (d) 12.7 J 7. In the question number 11, the work done by applied force is : (a) 10 J (b) 50 J (c) 100 J (d) 150 J 8. The correct relation between joule and erg is : (a) 1J 10 erg −5 = (b) 1J 10 erg 5 = (c) 1J 10 erg −7 = (d) 1J 10 erg 7 = 9. A weightlifter lifts a weight off the ground and holds it up : (a) Work is done in lifting as well as holding the weight (b) No work is done in both lifting and holding the weight (c) Work is done in lifting the weight but no work is required to done in holding it up) (d) No work is done in lifting the weight but work is required to be done in holding it up 10. A uniform chain of length 2 m is kept on a table such that a length of 60 cm hinges freely from the edge of the table. The total mass of the chain is 4 kg. The work done in pulling the entire chain on the table (Take 2 g ms − = ) (a) 12.9 J (b) 6.3 J (c) 3.6 (d) 2.0 J 11. 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, work required to pull the hanging part on to the table is : (a) MgL (b) 3 MgL (c) 9 MgL (d) 18 MgL 12. In the non-relativistic regime, if the momentum, is increased by 100%, the percentage increase in kinetic energy is : (a) 100 (b) 200 (c) 300 (d) 400 13. The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, then the mass of the air of density  passing through it in time t is : (a) Avt (b) 2Avt (c) Av t 2  (d) Av t 2 1  14. In the question number 21, the kinetic energy of the air is : (a) A vt 2 1  (b) A v t 2 1 2  (c) A v t 2 1 3  (d) 2A v t 3  15. Which of the following statements is incorrect? (a) Kinetic energy may be zero, positive or negative (b) Power, energy and work are all scalars (c) Potential energy may be zero, positive or negative (d) Ballistic pendulum is a device for measuring the speed of bullets 16. A 120 g mass has a velocity 1 jms ˆ i 5 ˆ v 2 − = +  at a certain instant. Its kinetic energy is : (a) 3 J (b) 4 J (c) 5 J (d) 1.74 J 17. The work done by a body against friction always results in : (a) Loss of kinetic energy (b) Loss of potential energy (c) Gain of kinetic energy (d) Gain of potential energy 18. The average energy consumed by a human being in a day is: (a) 2400 cal (b) 2400 J (c) 2400 KJ (d) 2400 Kcal 19. A truck and a car moving with the same kinetic energy are brought to rest by the application of brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance? (a) The truck (b) The car (c) Both will travel the same distance before coming to rest (d) Cannot be predicted 20. Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg wt. If they acquire the same kinetic energy in times t and t , A B then the ratio B A t t is : (a) 2 1 (b) 2 (c) 5 2 (d) 6 5
21. If the force acting on a body is inversely proportional to its speed, then its kinetic energy is : (a) Linearly related to time (b) Inversely proportional to time (c) Inversely proportional to the square of time (d) A constant 22. The area under force-displacement curve represents: (a) Velocity (b) Acceleration (c) Impulse (d) Work done 23. The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring to stretch it through an additional distance x? (a) 10 J (b) 20 J (c) 30 J (d) 40 J 24. Two men with weights in the ratio 4 : 3 run up a staircase in time in the ratio 12 : 11. The ratio of power of the first to that of second is: (a) 3 4 (b) 11 12 (c) 33 48 (d) 9 11 25. The potential energy of a system increases if work is done: (a) Upon the system by a non conservative force (b) By the system against a conservative force (c) By the system against a non conservative force (d) Upon the system by a conservative force 26. A ball bounces to 80% of its original height. What fraction of its mechanical energy is lost in each bounce? (a) 0.20 (b) 0.60 (c) 0.40 (d) 1 27. The negative of the work done by the conservative internal forces on a system equals to the change in: (a) Total energy (b) Kinetic energy (c) Potential energy (d) None of these 28. Which one of the following is not a conservative force? (a) Force of friction (b) Magnetic force (c) Gravitational force (d) Electrostatic force 29. Identify the false statement from the following: (a) Work-energy theorem is not independent of Newton’s second law (b) Work-energy theorem holds in all inertial frames (c) Work done by frication over a closed path is zero (d) Work done is a scalar quantity 30. A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to ( / ) 2 − k r where k is constant. The total energy of the particle is: (a) r k − (b) r k 2 − (c) r k 2 (d) r 2k 31. The bob of a pendulum is released from a horizontal position If the length of pendulum is 2 m, what is the speed with which the bob arrives at the lower most point. Assume that 10% of its energy is dissipated against air resistance: (Take 2 10 − g = ms ) (a) 1 4 − ms (b) 1 6 − ms (c) 1 8 − ms (d) 1 10 − ms 32. A ball of mass m is dropped from a cliff of height H. The ratio of its kinetic energy to the potential energy when it is fallen through a height H 4 3 is: (a) 3 : 4 (b) 4 : 3 (c) 1 : 3 (c) 3 : 1 33. Which of the following statements is incorrect? (a) Nowork is done if the displacement is perpendicular to the direction of the applied force (b) If the angle between the force and displacement vectors is obtuse, then the work done is negative (c) Frictional force is a non-conservation (d) All the central forces are non-conservative 34. The amount of energy released in burning 1 kg of coal is: (a) 3 MJ (b) 30 MJ (c) 300 MJ (d) 3000 MJ 35. Which of the following statements is correct? (a) Heat is absorbed in exothermic reaction (b) Heat is released in endothermic reaction (c) Energy released in burning 1 litre of gasoline is 300 MJ (d) Chemical energy is associated with the forces that give rise to the stability of substances 36. Energy required to break one bond in DNA is: (a) 10 J −10 (b) 10 J −18 (c) 10 J −7 ( d) 10 J −20 37. Which of the following units is not a unit of energy? (a) Kilowatt (b) Watt (c) Erg (d) Calorie 38. A man weighing 60 kg climbs up a staircase carrying a load of 20 kg on his head. The stair case has 20 steps each of height 0.2 m. If he takes 10 s to climb, find his power: (a) 313.6 W (b) 120.6 W (c) 510 W (d) 0 39. 1 kilowatt hour (k Wt) is equal to: (a) 2.25 10 eV 22  (b) 2.25 10 eV 23  (c) 2.25 10 eV 25  (d) 2.25 10 eV 27  40. A force k) ˆ j 2 ˆ i ˆ (4 + − N acting on a body maintains its velocity at 1 k)ms ˆ j 3 ˆ i 2 ˆ (2 − + − . The power exerted is: (a) 4 W b) 5 W (c) 2 W (d) 8 W 41. An elevator can carry a maximum load of 1800 kg (elevator + passengers) is moving up with a constant speed of 1 2 ms− . The frictional force opposing the motion is 4000 N. What is minimum power delivered by the motor to the elevator? (a) 22 kW (b) 44 kW (c) 66 kW (d) 88 kW 42. A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional to: (a) 1/ 2 t (b) t (c) 3/ 2 t (d) 2 t
43. A pump on the ground floor of a building can pump up water to fill a tank of volume 3 30 m in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump? (Take 2 g 10 ms− = ) (a) 36.5 kW (b) 44.4 kW (c) 52.5 kW (d) 60.5 kW 44. The power of a water pump is kW. If 2 g 10 ms− = , the amount of water it can raise in one minute to a height of 10 m is: (a) 2000 litre (b) 1000 litre (c) 100 litre (d) 1200 litre 45. Water is flowing in a river at 1 2ms− . The river is 50 m wide and has an average depth of 5 m. The power available from the current in the river is: (Density of water = 1000 kg m-3 ) (a) 0.5 MW (b) 1 MW (c) 1.5 MW (d) 2 MW 46. A spherical ball of mass m1 collides head on with another ball of mass m2 at read. The collision is elastic. The fraction of kinetic energy lost by m1 is: (a) 2 1 2 1 2 (m m ) 4m m + (b) 1 2 1 m m m + (c) 1 2 2 m m m + (d) (m m ) m m 1 2 1 2 + 47. Consider the following statements A and B. Identify the correct choice in the given answers: A. In a one dimensional perfectly elastic collision between two moving bodies of equal masses, the bodies merely exchange their velocities after collision B. If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity, then after collision both travel with same velocity (a) A and B are correct (b) Both A and B are wrong (c) A is correct, B is wrong (d) A is wrong, B is correct 48. When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after collision they will move: (a) Opposite to one another (b) In the same direction (c) Together (d) At right angle to each other 49. A ball falls under gravity from a height of 10 m with an initial downward velocity u. It collides with the ground, losses 50% of its energy in collision and then rises back to the same height. The initial velocity u is: (a) 1 7ms− (b) 1 25ms− (c) 1 14ms− (d) 1 28ms− 50. A ball of mass m moving with a speed 0 2v 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) 1 e 1 e + − (b) 1 e 1 e − + (c) e 1 e 1 + − (d) e 1 e 1 − + 51. A ball of mass m collides with a wall with speed v and rebounds on the same line with the same speed. If the mass of the wall is taken as infinite, then the work done by the ball on the wall is: (a) 2 mv (b) 2 mv 2 1 (c) 2mv (d) Zero 52. 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: (a) e h 2 (b) 2 eh (c) e h 4 (d) 4 e h 53. Fast neutrons can easily be slowed down by: (a) The use of lead shield (b) Passing them through heavy water (c) Elastic collision with heavy nucleus (d) Applying a strong electric field 54. An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because. (a) The two magnetic forces are equal and opposite, so they produce no net effect. (b) The magnetic forces do no work on each particle. (c) The magnetic forces do equal and opposite (but non – zero) work on each particle. (d) The magnetic forces are necessarily negligible. 55. A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one is which the charged particle is a proton and in another a positron. In the same time t, the work done on the two moving charged particles is. (a) Same as the same force law is involved in the two experiments. (b) Less for the case of a positron, as the positron moves away more rapidly and the force on it weakens. (c) More for the case of a positron, as the positron moves away a larger distance. (d) Same as the work done by charged particle on the stationary proton. 56. A man squatting on the ground gets straight up and stands. The force of reaction of ground on the man during the process is. (a) Constant and equal to mg in magnitude. (b) Constant and greater than mg in magnitude. (c) Variable but always greater than mg. (d) At first greater than mg, and later becomes equal to mg.
57. A bicyclist comes to a skidding stop in 10 m. during this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is (a) +2000 J (b) – 200 J (c) zero (d) – 20000 58. A body is falling freely under the action of gravity alone in vacuum which of the following quantities remain constant during the fall? (a) Kinetic energy (b) Potential energy (c) Total mechanical energy (d) Total linear momentum 59. 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 60. Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in figure. Which of the following statements is correct? (a) Both the stones reach the bottom at the same time but not with the same speed. (b) Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II. (c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I. (d) Both the stones reach the bottom at different times and with different speeds. 61. The potential energy function for a particle executing linear SHM is given by 2 kx 2 1 V(x) = where k is the force constant of the oscillator. For 1 k 0.5 Nm− = , the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x = x m . If V and K indicate the potential energy and kinetic energy, respectively of the particle at x = +x m then which of the following is correct? (a) V = 0, K = E (b) V = E, K = 0 (c) V < E, K = 0 (d) V = 0,K< E 62. Two identical ball bearings in contact with each other and resting on a frictionless table are hit head – on by another ball bearing of the same mass moving initially with a speed v as shown in figure. If the collision is elastic, which of the following is a possible result after collision? (a) (b) (c) (d) 63. A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement – time curve for its motion? (a) (b) (c) (d) 64. Which of the diagrams shows in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit? (a) (b) (c) (d) 65. Which of the diagrams shown in figure represents variation of total mechanical energy of a pendulum oscillation in air as function of time? (a) (b)