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t en nm nment sig ssig As A Assignment Assignment (1) 84 J (2) 24 J SECTION - A (3) 48 J (4) 100 J NCERT Based MCQs 4. A bullet having mass 10 g is fired towards a fixed 1. If the magnitude of two vectors are 8 unit and wooden block with velocity of 30 m/s. If it comes 5 unit and their scalar product is zero, the angle out of the block with velocity of 20 m/s, then the between the two vectors is [NCERT Pg. 114] total work done by the resistive forces is (1) Zero (2) 30° [NCERT Pg. 125] (3) 60° (4) 90° (1) –4.5 J (2) 2 J 2. In which of the following figures the work done by (3) –2.5 J (4) Zero force F in displacing an object through distance d  is positive? ( is the angle between F and d) 5. A force F  (3iˆ  4 jˆ  5kˆ ) N acts on an object and  [NCERT Pg. 116] displaces it through d  5kˆ m. The total work F done by the force in this process is [NCERT Pg. 117] (1) (1) 25 J (2) 60 J (3) 15 J (4) 20 J d 6. A body of mass m is raised to height h from Object ground along three different paths viz I, II and III F against gravity as shown below. If WI, WII and WIII are the work done along the respective paths of I, (2) II and III, then the correct option is (there is no non- conservative force) [NCERT Pg. 124]  d Path III Object F Path II (3) h  d Object Path I (4) (1) WIII > WII > WI (2) WI > WII > WIII F d Object (3) WII > WI > WIII (4) WI = WII = WIII 3. The figure given below shows the force F versus 7. Two balls, one of mass m and other of mass 2 m displacement x graph. The net work done by the are moving towards each other with respective force when an object is displaced from x = 0 to speeds of 10 m/s and 20 m/s on a smooth x = 16 m is NCERT Pg. 118] horizontal floor. If after collision they stick to each F(N) other and move as combined mass (perfectly inelastic collision), then the speed of combined mass will be [NCERT Pg. 129] 4 (1) 20 m/s (2) 10 m/s 0 x(m) (3) 30 m/s (4) 50 m/s 4 12 16 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 190 Work, Energy and Power NEET 8. An object of mass m moves on a circular track of 14. The power required by engine of car of mass radius R with constant speed u. The work done by 1000 kg to accelerate it from rest to a speed of centripetal force after it completes one circle is 72 km/h in 20 s is [NCERT Pg. 128] [NCERT Pg. 116] (1) 10 kW (2) 1 kW (1) 2mu2 (2) mu2 (3) 100 kW (4) 1000 kW (3) 2mu2 (4) Zero 15. A bullet of mass 100 g hits a block of thickness 9. A ball is dropped from 100 m and it rebounds to a 5 cm with a speed of 200 m/s. It emerges with height of 70 m. The percentage loss of energy is 10% of its initial kinetic energy. Then, its emergent speed will be [NCERT Pg. 125] [NCERT Pg. 125] (1) 30% (2) 70% (1) 20 10 m/s (2) 20 3 m/s (3) 60% (4) 10% (3) 20 m/s (4) 10 10 m/s 10. A moving body has kinetic energy twice its momentum. The speed of the body is 16. A stone of mass 2 kg tie with the help of thread of [NCERT Pg. 119] length 2 m and moves in vertical circular motion. The difference between tension in the thread at lowest (1) 2 m/s (2) 2 m/s point and at the highest point is (Take g = 10 m/s2) [NCERT Pg. 122] (3) 4 m/s (4) 3 m/s (1) 60 N (2) 120 N 11. A body of mass 1 kg is moving with velocity of (3) 30 N (4) 240 N (3iˆ  4 ˆj ) m/s. The kinetic energy possessed by it will be [NCERT Pg. 119] 17. A body is released from position A as shown in figure. The speed of body at position B is (1) 125 J (2) 25 J [NCERT Pg. 121] (3) 10.8 J (4) 12.5 J 12. The figure below shows a fixed smooth incline A plane having slope length l, height h and base length b. It is attached to a smooth horizontal ground. 50 m B A block of mass m is released from top of a plane. 10 m On reaching the bottom of incline plane, the kinetic energy possessed by it is [NCERT Pg. 121] (1) 10 m/s (2) 10 2 m/s m l (3) 20 m/s (4) 20 2 m/s h 18. A ball of 4 kg mass moving with velocity 40 m/s in east direction collides with another ball of 6 kg mass moving with velocity 20 m/s in east direction. Smooth horizontal plane b After collision two balls stick together, then loss of kinetic energy is [NCERT Pg. 129] (1) mgl (2) mgb (1) 360 J (2) 240 J (3) mgh (4) mg(l + h) (3) 480 J (4) 600 J 13. If symbols have their usual meanings, then which of the following relations is true for equilibrium of a 19. Which quantity remains conserved in all types of particle? [NCERT Pg. 120] collisions? [NCERT Pg. 129] (1) Linear momentum dU dU (1) 0 (2) 0 dr dr (2) Kinetic energy dU dU (3) Potential energy (3) 0 (4)  k , (k  0) dr dr (4) Both (1) & (2) Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 NEET Work, Energy and Power 191 20. A chain of mass 2 kg is placed on a smooth table SECTION - B 1 with th of its length hanging over the edge. 4 Objective Type Questions If the length of chain is 4 m then the work done in 1. The work done in extending a spring by l0 is w0. pulling the hanging portion of the chain back to the The work done in further extenstion l0 will be surface of the table is [NCERT Pg. 118] (1) 3w0 (2) 2w0 (1) 5 J (2) 2.5 J (3) 2 J (4) 4 J w0 w0 (3) (4) 2 4 21. If momentum of a body is decreased by 50%, then kinetic energy will be decreased by 2. A body is subjected to a constant force given by  [NCERT Pg. 119] F (N )  iˆ  2 ˆj  3kˆ. What is the work done by (1) 25% (2) 50% this force in moving the body through a distance of 4m along the z-axis and then 3m along the y-axis? (3) 75% (4) 125% (1) 18 J (2) 12 J 22. Internal force cannot change [NCERT Pg. 121] (3) 16 J (4) Zero (1) Kinetic energy 3. The distance X moved by a body of mass 0.5 kg (2) Total momentum of system under the action of a force varies with time t as (3) Total energy of system x(m) = 3t2 + 4t + 5 (here t is expresed in second). (4) All of these What is the work done by the force in first 2 seconds? 23. Select correct statement regarding stable equilibrium. [NCERT Pg. 121] (1) 20 J (2) 40 J (1) Potential energy of body is minimum in stable (3) 50 J (4) 60 J equilibrium 4. A particle of mass 0.5 kg is subjected to a force (2) Slope of potential energy versus position graph which varies with distance as shown in graph is zero at stable equilibrium F (N) (3) A restoring force acts on the body when it is slightly displaced from its stable equilibrium 10 position X (m) (4) All of these 4 8 12 24. In a conservative field, the potential energy U as a If the speed of the particle at x = 0 is 4 m/s, then function of position x is given by U = x2. Then the its speed at X = 8 m is corresponding conservative force is given by (1) 8 m/s (2) 16 m/s [NCERT Pg. 121] (3) 32 m/s (4) 4 m/s (1) x (2) 2x x  (3) –x (4) –2x 5. The force exerted on an object is F  f0   1. a  25. If a mass m collides elastically with another Find the work done in moving the object from identical mass at rest in oblique manner, then x = 0 to x = 3a. after collision both the masses move at an 3 angle of [NCERT Pg. 131] (1) f0 a 2 (1) 30° 1 (2) 45° (2) f0 a 2 (3) 60° (3) f0 a (4) 90° (4) Zero Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 192 Work, Energy and Power NEET 6. The work done in moving a particle from a point 12. An elastic ball at rest with coefficient of (1, 1) to (2, 3) in a plane in force field with 1 potential U = k(x + y) is restitution is dropped from a height h on a 2 (1) 3k (2) –3k smooth floor. The total distance covered by the ball (3) k (4) Zero is 7. A ball (100 gm) thrown from ground with speed 5 (1) h (2) 5h 20 m/s comes back to the ground with speed 3 10 m/s. Find the work done by air resistance. 4 (1) 15 J (2) 20 J (3) 3h (4) h 3 (3) 30 J (4) 40 J 13. A block of mass m moving at a speed v 8. In a certain field, the potential energy is U =ax2 – compresses a spring through a distance x before bx3, where a and b constants. The particle is in its speed is halved. Find the spring constant of the stable equilibrium at x equal to spring. a mv 2 3mv 2 (1) Zero (2) (1) (2) 3b 4x 2 x2 2a 2a 4mv 2 3mv 2 (3) (4) (3) 2 (4) 3b b 3x 4x2 9. A ball of mass m moving at a speed v makes a 14. A particle is thrown with kinetic energy k straight head on collision with an identical ball at rest. The up a rough inclined plane of inclination  and kinetic energy of the ball after the collision is 4% coefficient of friction . The work done against of the original. Find the coefficient of restitution. friction before the particle comes to rest is 3 2 k sin  k cos  (1) (2) (1) (2) 5 5 cos    sin  cos    sin  1 1 k sin  k cos  (3) (4) 5 3 (3) sin    cos  (4) sin    cos  10. In head on elastic collision of two bodies of equal 15. A ball of mass m is thrown from ground with speed masses u at an angle  with horizontal. Find the power (1) The velocities are interchanged when the ball is at maximum height of the (2) The speeds are interchanged trajectory (3) The momenta are interchanged mgu (1) (2) mgucos (4) All of these cos  11. A pendulum bob of mass M is raised to a height (3) mgusin (4) Zero h and then released. At the bottom of its swing, it 16. The ball of mass m is thrown with speed v 0. picks up a mass m. To what height will the The ball strikes the block of mass 2m and sticks combined mass rise? to it. Find the maximum compression of spring. m2 h (1)  m  M 2 V0 k 2 M h m 2m (2)  m  M 2 Smooth mMh m m (3) m  M  (1) v 0 (2) v 0 3k 2k mMh 2m 3m (4)  m  M 2 (3) v 0 (4) v 0 k k Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 NEET Work, Energy and Power 193 17. A ball is thrown from the ground with velocity u at 22. A particle of mass m moves on a straight line with an angle  with horizontal. The horizontal range of its velocity varying with the distance travelled. If the the ball on the ground is R. If the coefficient of relation between velocity and distance is v = Kx (K restitution is e, then the horizontal range after the is constant), then find the work done by the forces collision is during a displacement x = 0 to x = d. (1) e3 R (2) e2 R mkd 2 mk 2d 2 R (1) (2) (3) eR (4) 2 2 e 18. A particle of mass m strikes another particle of mk 3 d 2 md 3 k 3 (3) (4) same mass at rest elastically. After collision if 2 2 velocity of one of the particle is 3iˆ – 2 jˆ m/s , then 23. A body is initially at rest. It undergoes one the other must have a velocity equals to dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (1) iˆ  jˆ (2) 2iˆ  3 ˆj 1 (3) 2iˆ – jˆ (4) iˆ  3 jˆ (1) t 2 (2) t 19. A particle of mass m moving with horizontal speed 3 6 m/s collides elastically with another particle of mass (3) t 2 (4) t2 M (m