Title WORK ENERGY AND POWER.pdf ✅

6.WORK ENERGY AND POWER Single Correct Answer Type 1. The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is a) 968 J b) 98 J c) 1980 J d) None of these 2. 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 3. One man takes 1 minute to raise a box to a height of 1 m and another man takes minute to do so. The 1 2 energy of the two is a) Different b) Same c) Energy of the first is more d) Energy of the second is more 4. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = ,where and are constants and is the distance between the atoms. If the a x 12 − b x 6 a b x dissociation energy of the molecule is D = [U(x = ∞) − U , is at equilibrium ] D a) b 2 6a b) b 2 2a c) b 2 12a d) b 2 4a 5. If the kinetic energy of a body is increased 2 times , its momentum will a) Half b) Remain unchanged c) Be doubled d) increase 2 times 6. A steel ball of radius 2 cm is at rest on a frictionless surface. Another ball of radius 4 cm moving at a velocity of 81 cm/sec collides elastically with first ball. After collision the smaller ball moves with speed of a) 81 cm/sec b) 63 cm/sec c) 144 cm/sec d) None of these 7. If W and represent the work done in moving a particle from to along three different paths 1, 2 1 , W 2 W 3 A B and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W and 1 , W 2 W 3 a) W 1 > W 2 > W 3 b) W 1 = W 2 = W 3 c) W 1 < W 2 < W 3 d) W 2 > W 1 > W 3 8. Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of 45 2 ms each, the velocity of −1 their combined after collision is a) 45 2 ms −1 b) 45 ms −1 c) 90 ms −1 d) 22. 5 2 ms −1 9. A man does a given amount of work in 10 s. Another man does the same amount of work in 20 s. The ratio of the output power of first man to the second man is Page| 1
a) 1 b) 1 2 c) 2 1 d) None of these 10. 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) W 2 = 2W 1 2 b) W 2 = 2W 1 c) W 2 = W 1 d) W 2 = 0. 5W 1 11. The potential energy of a particle in a force field is U = , where and are positive constants and A r 2 − B r A B r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is a) B/2A b) 2A/B c) A/B d) B/A 12. Consider the following statements. A and B and identify the correct answer given below. I. Body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time. II. When a body is at rest, it must be in equilibrium. a) A and B are correct b) A and B are wrong c) A is correct and B is wrong d) A is wrong and B is correct 13. A body at rest breaks into two pieces with unequal mass a) Both of them have equal speeds b) Both of them move along a same line with unequal speeds c) Sum of their momentum is non zero d) They move along different lines with different speeds 14. A mass of 50 kg is raised through a certain height by a machine whose efficiency is 90%, the energy is 5000 J. If the mass is now released, its KE on hitting the ground shall be a) 5000 J b) 4500 J c) 4000 J d) 5500 J 15. A body of mass 2 kg is projected at 20 m/s at an angle of 60°above the horizontal. Power on the block due to the gravitational force at its highest point is a) 200 W b) 100 3 W c) 50 W d) Zero 16. An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine a) 800 W b) 400 W c) 200 W d) 100 W 17. A particle free to move along the x-axis has potential energy given by U(x) = k[1 − exp exp − x for 2 ( ) ] − ∞≤x≤ + ∞, where k is a positive constant of appropriate dimensions. Then a) At point away from the origin, the particle is in unstable equilibrium b) For any finite non-zero value of x, there is a force directed away from the origin c) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin d) For small displacements from x = 0, the motion is simple harmonic 18. The relation between the displacementX of an object produced by the application of the variable force F is represented by a graph shown in the figure. If the object undergoes a displacement from X = 0. 5 m to X = 2. 5 m the work done will be approximately equal to Page| 2
a) 16 J b) 32 J c) 1. 6 J d) 8 J 19. Two rectangular blocks A and B of masses 2kg and 3 kg respectively are connected by spring of spring constant 10.8 Nm and are placed on a frictionless horizontal surface. The block was given an initial −1 A velocity of 0.15 ms in the direction shown in the figure. The maximum compression of the spring during −1 the motion is a) 0.01 m b) 0.02 m c) 0.05 m d) 0.03 m 20. A force of 5N, making an angle θ 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 21. The 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 22. A 10 H. P. motor pumps out water from a well of depth 20m and fills a water tank of volume 22380 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is ( g = 10ms ) −2 a) 5 minutes b) 10 minutes c) 15 minutes d) 20 minutes 23. Power of water pump is 2 kW. If g = 10 m/sec , the amount of water it can raise in one minute to a height 2 of 10 m is a) 2000 litre b) 1000 litre c) 100 litre d) 1200 litre 24. A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to1. 8 m. The ball loses its velocity on bouncing by a factor of a) 16/25 b) 2/5 c) 3/5 d) 9/25 25. A coolie 1.5 m tall raises a load of 80 kg in 2 s from the ground to his head and then walks a distance of 40 m in another 2 s. The power developed by the coolie is [g = 10 ms −2 ] a) 0.2 kW b) 0.4 kW c) 0.6 kW d) 0.8 kW 26. A bomb at rest explodes into 3 parts of the same mass. The momentum of the 2 parts is − 2pIand . The momentum of the third part will have a magnitude of ^ pj ^ a) p b) 3p c) p 5 d) zero 27. The potential energy of a certain spring when stretched through a distance s is 10 J. The amount of work (in joule) that must be done on this spring to stretch it through additional distance s will be a) 30 b) 40 c) 10 d) 20 Page| 3
28. A particle of mass m moving with horizontal speed 6 m/sec as shown in figure. If m << M than for one dimensional elastic collision, the speed of lighter particle after collision will be a) 2m/sec in original direction b) 2m/sec opposite to the original direction c) 4m/sec opposite to the original direction d) 4m/sec in original direction 29. 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 θ 1 and θ respectively with the initial direction of motion. 2 The sum of the angles θ 1 + θ 2 a) 45° b) 90° c) 135° d) 180° 30. A car weighing 1400 kg is moving at a speed of 54 kmh up a hill when the motor stops. If it is just able to −1 reach the destination which is at a height of 10 m above the point, then the work done against friction (negative of the work done by the friction) is [Take g = 10ms ] −2 a) 10 kJ b) 15 kJ c) 17.5 kJ d) 25 kJ 31. A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1gand 3g. The total K.E. of the fragments is 6. 4×10 . What is the K.E. of the smaller fragment 4 J a) 2. 5×10 4 J b) 3. 5 ×10 4 J c) 4. 8 ×10 4 J d) 5. 2 ×10 4 J 32. If the heart pushes 1 cc of blood in 1 s under pressure 20000Nm ,the power of heart is −2 a) 0.02 W b) 400 W c) 5× 10 W −10 d) 0.2 W 33. The energy required to accelerate a car from 10 m/s to 20 m/s is how many times the energy required to accelerate the car from rest to 10 m/s a) Equal b) 4 times c) 2 times d) 3 times 34. A uniform chain of length L and mass Mis 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) MgL/3 c) MgL/9 d) MgL/18 35. When a 1. 0 kg 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/s 2 a) 1. 5 joule b) 2. 0 joule c) 2. 5 joule d) 3. 0 joule 36. A mass m is attached to the end of a rod of length l. The mass goes around a vertical circular path with the other end hinged at the centre. What should be the minimum velocity of mass at the bottom of the circle, so that the mass complete the circle? a) 4gl b) 3gl c) 5gl d) gl 37. A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is a) c a+b . b b) a a+c . b c) a+b c . a d) a+c a . b Page| 4