WORK POWER ENERGY-04-OBJECTIVE UNSOLVED

1. A force →  k(yˆi  xˆj) , where k is a positive constant, acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0), and the parallel to the y-axis to the point (a, a). The total work done by the force on the particle is (a) (c)  2ka 2  ka 2 (b) (d) 2ka 2 ka 2 . 2. Supposing that the earth of mass m moves around the sun in a circular orbit of radius ‘R’, the work done in half revolution is mv2 (a) R R (b) mv2 R  2R (c) Zero (d) none of these 3. When water falls from the top of a water fall 100 m high (a) it freezes (b) it warms up slightly (c) it evaporates (d) there is no change in temperature. 4. A string of mass ‘m’ and length ‘l’ rests over a frictionless table with 1/4th of its length hanging from a side. The work done in bringing the hanging part back on the table is (a) mgl/4 (b) mgl/32 (c) mgl/16 (d) none of these 5. A weight mg is suspended from a spring. If the elongation in the spring is x0, the elastic energy stored in it is (a) 1 mgx 2 0 (b) 2mgx0 (c) mgx0 6. Mechanical Energy is conserved under (d) 1 mgx 4 0 (a) Conservative system of forces (b) disipative forces (c) (a) and (b) (d) none of these 7. The same retarding force is applied to stop a train. If the speed is doubled then the dis- tance will be (a) eight times (b) doubled (c) half (d) four times 8. 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) 1 m v t2 (b) m v t2 2 t1 t1 (c) 1  mv t  t2 (d) 1 v2 m t 2   2  1  1 9. A particle moves under the effect of a force F = kx2 from x = 0 to x = 4 the work done by force is 8k (a) 3 64k (c) 3 32k (b) 3 128k (d) 3 10. Potential energy function describing the interaction between two atoms of a diatomic molecule is U(r)  a  b r12 r6 Force acting between them will be zero when the distance between them would be  2a 1/6  b 1/ 6 (a)  b  (b)  2a       a 1/ 6 (c)  b   b 1/ 6 (d)  a      11. A ball is thrown up with a certain velocity at angle  to the horizontal. The kinetic energy KE of the ball varies with horizontal displacement x as: (a) KE (b) KE O O x x (c) KE O (d) KE O 12. A body m1 is projected upwards with velocity v1 another body m1 of same mass is projected at an angle of 450. Both reach the same height. What is the ratio of their kinetic energies at the point of projection (a) 1 (b) 1/2 (c) 1/3 (d) 1/4 13. A 2kg block is dropped from a height of 0.4 m on a spring of force constant 2000N/m. The maximum compression of the srpring is:- (a) 0.1 m (b) 0.2 m (c) 0.01 m (d) 0.02 m 14. The kinetic energy of body is increased by 300% its momentum will be increased by (a) 100% (b) 200% (c) 300% (d) 400% 15. A particle of mass M is moving in a horizontal circle of radius ‘R’ under the centripetal force equal to K/R2, where K is constant. The potential energy of the particle is (a) K/2R (b) -K/2R (c) K/R (d) -K/R LEVEL - II 1. An object of mass m is tied to a string of length l and a variable horizontal force is applied on it which is initially is zero and gradually increases until the string makes an angle  with the vertical. Workdone by the force F is F (a) mgl(1 – sin) (b) mgl (c) mgl(1 – cos) (d) mgl(1 + cos ) 2. A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is – (a) 3mg (b) 4mg (c) 5 mg (d) 6 mg 3. A horse pulls a wagon with a force of 360 N at an angle of 60º with the horizontal at a speed of 10 Km/hr. The power of the horse is (a) 1000 W (b) 2000 W (c) 500 W (d) 750 W. 4. A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be (a) zero (b) (c) (d) 5. A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length l. The system is rotated about the other end of the spring with an angular velocity , in gravity free space. The increase in length of the spring will be – m2l (a) k m2l (b) m2l k - m2 (c) k  m2 (d) none of these 6. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time as ac = k rt , where k is a constant. The power delivered 2 2 to the particle by the forces acting on it is – (a) 2 mk2r2t (b) mk2r2t 1 (c) 3 mk4r2t5 (d) 0 7. In the figure shown, the net work done by the tension when the bigger block of mass M touches the ground is – (a) + Mgd (b) – (M + m) gd (c) – Mgd (d) zero 8. 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) 2 M (b) M (c) M/2 (d) a function of M and the force constant of the spring 9. A man pulls a bucket of water from a well of depth H. If the mass of the rope and that of the bucket full of water are m and M respectively, then the work done by the man is–  m  M (a) (m + M)gh (b)    gh   m  M  gh m  M  (c)    2  (d)    gh  10. 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– mv2 (a) mg (b) mg – R mv2 (c) mg + R (d) zero. 11. A small block of mass m is kept on a rough inclined surface of inclination  fixed in a elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in time t will be – (a) zero (b) mgvt cos2 (c) mgvt sin2 (d) mgvt sin 2 12. 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 – 1 1 (a) 2 kx2 (b) – 2 kx2 1 1 (c) 4 kx2 (d) – 4 kx2 13. A bent bow used for shooting an arrow possesses : (a) Kinetic Energy (b) Potential Energy (c) Heat Energy (d) Chemical Energy. 14. A block of mass m moving with speed v compresses a spring through distance x before its speed is halved. What is the value of spring constant ? (a) (c) 3mv2 4x2 mv2 2x2 (b) (d) mv2 4x2 2mv2 x2 15. A ball falls under gravity from a height 10 m with an initial velocity v0. It hits the ground, losses 50% of its energy in collision and it rises to the same height. What is the value of v0 ? (a) 14 m/s (b) 7 m/s (c) 28 m/s (d) 9.8 m/s.