Title 03A. WORK POWER ENERGY ( 55 - 70 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 5 5 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY SYNOPSIS 1. Work is related with state of energy of a body. 2. Work in mechanics is strictly a rigid body or point object phenomena or we can define the work as “It’s the dot product of force and displacement of point of application due to that force.” 3. Average power delivered by a variable power source in a given time t. pdt P dt      LEVEL-V SINGLE ANSWER TYPE QUESTIONS 1. The displacement x in metre 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   2 x t   3 . The work done by the force (in joules) in first six seconds is A) 18 m B) zero C) 9m/2 D) 36 m 2. A pump motor is used to deliver water at a certain rate from a given pipe. To obtain n times of amount of water from the same pipe in the same time, by what amount should the power of the motor be increased. A) 2 n times B) 3 n times C) n times D) 3/2 n times 3. The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by A) 3xP v m  B) 3/2 3xP v m        C) 1/3 3xP v m        D) 2 3xP v m        4. A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. The car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is (A) mg (B) mg – R mv2 (C) mg + R mv2 (D) zero. 5. A block of mass m is moving with a constant acceleration a on a rough plane. If the coefficient of friction between the block and the ground is  , the power delivered by the external agent after a time t from the beginning of motion is equal to A) 2 ma t B) mgat C)   m a g gt    D) m a g at     6. Which of the following graphs represents the variation of kinetic energy of a ball bouncing on a horizontal floor with height? (Neglect air resistance). A) B) C) D) KE does not vary with ‘h’ WORK POWER ENERGY
5 6 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY 7. A particle of mass m is projected at an angle  to the horizontal with an initial velocity u. the work done by gravity during the time it reaches its highest point is A) 2 2 u sin  B) 2 2 cos 2 mu  C) 2 2 sin 2 mu  D) 2 2 sin 2 mu   8. A particle located in a one-dimensional potential field has its potential energy function as   4 2 a b U x x x   , where a and b are positive constants. The position of equilibrium x corresponds to A) 2 b a B) 2a b C) 2b a D) 2 a a 9. A particle of mass m moves with a variable velocity v, which changes with distance covered x along a straight line as v k x  , where k is a positive constant. The work done by all the forces acting on the particle, during the first t seconds is A) 4 2 mk t B) 4 2 4 mk t C) 4 2 8 mk t D) 4 2 16 mk t 10. A uniform chain AB of mass m and length l is placed with one end A at the highest point of a hemisphere of radius R. referring to the top of the hemisphere as the bottom level, the potential energy of the chain is (given that 2 R l   ). A) 2 1 sin mR g l l R R       B) 2 sin 2 mR g l l l R R        C) 2 sin 2 mR g l l l R R        D) 2 sin mR g l l l R R        11. A particle is projected along a horizontal surface whose coefficient of friction varies as 2 A r   , where r is the distance from the origin in metres and A is a positive constant. The initial distance of the particle is 1m 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 gA c) 2gA d) 4 gA 12. In fig, the potential energy U of a particle is plotted against its position x from origin. Which of the following statements is correct? A) 1 x is in stable equilibrium B) 2 x is in stable equilibrium C) 3 x is in stable equilibrium D) 1 x is in neutral equilibrium 13. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t1 as a function of time t is given by (A) 2 1 t t v m 2 1 (B) 2 1 t t v m (C) 2 2 1 t t t mv 2 1         (D) 2 2 1 2 t t v m 2 1 14. A particle moves under the effect of a force F = kx2 from x = 0 to x = 4 the work done by force is (A) 3 8k (B) 3 32k (C) 3 64k (D) 3 128k
NISHITH Multimedia India (Pvt.) Ltd., 5 7 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY 15. In the figure, a ball a is released from rest when the spring is at its natural (unstretched) length. For the block B, of mass M to leave contact with the ground at some stage, the minimum mass of A must be A B M (A) 2 M (B) M (C) M/2 (D) a function of M and the force constant of the spring 16. A force    F xy z j zi    3 5 4   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. is A) 280 5 units B) 140 5 units C) 232 5 units D) 192 5 units 17. A sphere of mass 2 kg is moving on a frictionles horizontal table with velocity v. It strikes with a spring (force constant = 1 N/ m) and compresses is by 4m. The velocity v of the sphere is (A) 4 m/s (B) 2 2 m/s (C) 2 m/s (D) 2 m/s 18. A cord is used to lower vertically a block of mass M a distance d at a constant downward accleration of 4 g . Then the work done by the cord on the block is (A) 4 d Mg (B) 3 4 d Mg (C) – 3 4 d Mg (D) Mgd 19. A particle is being acted upon by one dimensional conservative force. In the F–x curve shown, four points A, B, C, D are marked on the curve. (a) State which type of equilibrium is the particle have at position c. •A B •C • x D O F A) stable equilibrium B) unstable C) Neutral D) No equilibrium 20. Displacement-time graph of a particle moving in a straight line is shown in figure. Determine in which of the following region OA, AB & BC work done by all the forces, is zero. A) OA B) AB C) BC D) ABC 21. A particle of mass 10 7 kg is moving in the positive direction of x. Its initial position is x = 0 & initial velocity is 1 m/s. The velocity at x = 10 is: (use the graph given) A) 4 m/s B) 2 m/s C) 3 2 m/s D) 100/3 m/s 22. The potential energy of a particle is determined by the expression   2 2 U x y    , where  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 B) 24 C) 16 D) Zero
5 8 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY 23. An engine is pulling a train of mass m on a level track at a uniform speed u. The resistive force offered per unit mass is f. A) Power expended by the engine is “mfu”. B) The extra power developed by the engine engine to maintain a speed u up a gradient of h in s is mghu s C) The frictional force exerting on the train is mf on the level track D) None of above is correct 24. A body of mass m slides downwards along a plane inclined at an angle  . The coefficient of friction is  . The rate at which kinetic energy plus gravitational potential energy dissipates expressed as a function of time is A)  mtg2 cos B)  mtg2 cos (sin – m cos ) C)  mtg2 – sin D)  mtg2 sin (sin – m cos ) 25. An elastic string of unstretched length L and force constat k is stretched by a small lengthx. It is further stretched by another small length y. The work done in the second stretching is : A) 2 1 ky2 B) 2 1 k(x2 + y2 ) C) 2 1 k (x + y)2 D) 2 1 ky (2x + y) 26. A rope ladder with a length l carrying a man with a mass m at its end is attached to the basket of ballon with a mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the baloon descends by a height h. Then the potential energy of the man (A) increases by mg l h   (B) increases by mgl (C) increases by mgh (D) increases by mg (2l –h) 27. Power applied to a particle varies with time as P = 2 (3 2 1) t t   watt, where t is in second. Find the change in its kinetic energy between time t = 2 s and t = 4s (A) 32J (B) 46J (C) 61 J (D) 102 J 28. A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x=0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x? (A) U x (B) U x (C) U x (D) U x 29. Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled a part 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 1 kx2 (B) – 2 1 kx2 (C) 4 1 kx2 (D) – 4 1 kx2 30. A block of mass m is allowed to slide down a fixed smooth inclined plane of angle q and length  . The magnitude of power developed by the gravitational force when the block reaches the bottom is (A) 2 3 2m (gsin )   (B) 3 2 (2 / 3)m g sin   (C) 2 2 (2 / 3)m g cos   (D) 3 2 (1/ 3)m g sin   31. An object of mass (m) is located at the origin of a vertical plane . The body is projected at an angle  with velocity V. The mean power developed by the gravitational force during the interval of time till it reaches maximum height (A) mgu sin (B) sin 2 mgu  (C) sin 3 mgu  (D) sin 4 mgu 