Title 05. NEWTONS LAWS OF MOTION Hard.pdf ✅

1. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is (a) o 60 (b) o 120 (c) o 150 (d) o 90 2. A light string passing over a smooth light pulley connects two blocks of masses m1 and m 2 (vertically). If the acceleration of the system is g/8 then the ratio of the masses is (a) 8 : 1 (b) 9 : 7 (c) 4 : 3 (d) 5 : 3 3. A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given g = 10 ) −2 ms (a) 2 100 − ms (b) 2 3 − ms (c) 2 10 − ms (d) 2 30 − ms 4. Two masses m1 and m 2 are attached to a string which passes over a frictionless smooth pulley. When 10 , 1 m = kg 6 , 2 m = kg the acceleration of masses is (a) 20 2 m / s (b) 2 5m / s (c) 2.5 2 m / s (d) 2 10 m / s 5. In the adjoining figure m1 = 4m2. The pulleys are smooth and light. At time t = 0, the system is at rest. If the system is released and if the acceleration of mass m1 is a, then the acceleration of m2 will be (a) g (b) a (c) 2 a (d) 2a 6. The acceleration of block B in the figure will be (a) (4 ) 1 2 2 m m m g + (b) (4 ) 2 1 2 2 m m m g + (c) ( 4 ) 2 1 2 1 m m m g + (d) ( ) 2 1 2 1 m m m g + 7. A block A with mass 100 kg is resting on another block B of mass 200 kg. As shown in figure a horizontal rope tied to a wall holds it. The coefficient of friction between A and B is 0.2 while coefficient of friction between B and the ground is 0.3. The minimum required force F to start moving B will be (a) 900 N (b) 100 N (c) 1100 N (d) 1200 N 8. A 20 kg block is initially at rest on a rough horizontal surface. A horizontal force of 75 Nis required to set the block in motion. After it is in motion, a horizontal force of 60 N is required to keep the block moving with constant speed. The coefficient of static friction is (a) 0.38 (b) 0.44 (c) 0.52 (d) 0.60 9. A block of mass M is placed on a rough floor of a lift. The coefficient of friction between the block and the floor is . When the lift falls freely, the block is pulled horizontally on the floor. What will be the force of friction (a)  Mg (b)  Mg/2 (c) 2 Mg (d) None of these 10. A body of 5 kg weight kept on a rough inclined plane of angle 30o starts sliding with a constant velocity. Then the coefficient of friction is (assume g = 10 m/s2 ) (a) 1 / 3 (b) 2 / 3 (c) 3 (d) 2 3 11. The upper half of an inclined plane of inclination  is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given (a)  = sin  (b)  = cot  (c)  = 2 cos (d)  = 2 tan  12. What is the maximum value of the force F such that the block shown in the arrangement, does not move (  = 1 / 2 3 ) A B F m1 m2 A B m1 m2 20 cm m1 m2 10 kg 6 kg B A
(a) 20 N (b) 10 N (c) 12 N (d) 15 N 13. A block of mass m rests on a rough horizontal surface as shown in the figure. Coefficient of friction between the block and the surface is . A force F = mg acting at angle  with the vertical side of the block pulls it. In which of the following cases the block can be pulled along the surface (a) tan    (b) cot   (c) tan  / 2   (d) cot / 2   14. A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2, while that between B and floor is 0.5. When a horizontal force of 25 N is applied on the block B, the force of friction between A and B is (a) Zero (b) 3.9 N (c) 5.0 N (d) 49 N 15. An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle  with the vertical, the maximum possible value of  is given by (a) cot = 3 (b) tan  = 3 (c) sec = 3 (d) cosec = 3 16. Two blocks of mass M1 and M2 are connected with a string passing over a pulley as shown in the figure. The block M1 lies on a horizontal surface. The coefficient of friction between the block M1 and horizontal surface is . The system accelerates. What additional mass m should be placed on the block M1 so that the system does not accelerate (a)  M2 − M1 (b) 1 2 M M −  (c)  1 2 M M − (d) (M2 − M1 ) 17. The coefficient of kinetic friction is 0.03 in the diagram where mass m2 = 20 kg and m1 = 4 kg . The acceleration of the block shall be ( 10 ) −2 g = ms (a) 1.8 −2 ms (b) 0.8 −2 ms (c) 1.4 −2 ms (d) 0.4 −2 ms Q 18. A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is (a) 20% (b) 25% (c) 35% (d) 15% 19. The system shown in the figure is in equilibrium. The maximum value of W, so that the maximum value of static frictional force on 100 kg. body is 450 N, will be (a) 100 N (b) 250 N (c) 450 N (d) 1000 N 20. A smooth block is released at rest on a 450 incline and then slides a distance d. The time taken to slide is n times a much to slide on a rough incline plane than on a smooth incline. The coefficient of friction is (a) k = 1 - 2 n 1 (b) k = 2 n 1 1− (c) s = 1 - 2 n 1 (d) s = 2 n 1 1− 21. The upper half of an inclined plane with inclination  is perfectly smooth. While the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by (a) 2 sin  (b) 2 cos (c) 2 tan  (d) tan  22. A block is kept on a frictionless inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to(a) g/tan  (a) g/tan  (b) g cosec  (c) g (d) g tan  23. A particle of mass 0.3 kg is subjected to a force F = kx with k = 15 N – m-1 . What will be its initial acceleration if it is released from a point 20 cm away from the origin? (a) 3 ms-2 (b) 15 ms-2 (c) 5 ms-2 (d) 10 ms-2 W 45o 100 kg m1 20 kg m2 T T 4 kg M2 M1 m   m mg = F 60o F m = 3kg
24. The adjacent Fig. is the part of a horizontally stretched net. Section AB is stretched by 10N. The tension in the section BC and BG are (a) 10 N, 11 N (b) 10 N, 6 N (c) 10 N, 10 N (d) Cannot be determined 25. In the fig shown, a cubical block is held stationary against a rough wall by applying force F then incorrect statement among the following is (a) Frictional force f = Mg (b) F = N, N is Normal reaction (c) F does not apply any torque (d) N does not apply any torque. 26. A block of mass m is placed on a smooth wedge of inclination . The whole system is accelerated horizontally so that block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude. (a) mg (b) mg cos (c) mg/cos (d) mg tan 27. A person standing on the floor of an elevator drops a coin. The coin touches the floor of the elevator in time t, which the elevator is stationary and time t2 when elevator is moving uniformly then depends whether lift is moving up or down. (a) t1 = t2 (b) t1> t2 (c) t1< t1 (d) t1> t2 or t1< t2 28. A boat of mass 300 kg moves according to the equation x = 1.2 t 2 – 0.2 t3 . When the force will become zero? (a) 2s (b) 1 s (c) 6s (d) 2.8 s 29. A ball falls from a height h in a fluid which offers a resistance f = -kv. Find the terminal velocity if mass of the ball is m (a) k mg (b) k mgh (c) k mg − B (d) None of these 30. Assuming coefficient of friction 0.25 between block and incline. Find the acceleration of each block in fig. (a) g/5 (b) g/7 (c) g/6 (d) None of these 31. An 8 kg block of ice, released from rest at the top of a 1.5 m long smooth ramp, slides down and falls with a velocity 2.5 ms- 1 . Find angle of the ramp with horizontal. (a) 120 (b) 180 (c) 150 (d) 300 32. A 60 kg boy stands on a scale in the elevator. The elevator starts moving and records 450N. Find the acceleration of the elevator. (a) 2.5 ms-2 upward (b) 2.5 ms-2 downwards (c) 2.5 ms-2 in either direction (d) None of these 33. A weight W is lifted by applying a force F as shown in Fig. Find F in terms of W. Assume constant velocity. (a) F = W (b) F = 2W (c) F = W/2 (d) None of these 34. A window scrubber is used to brush up a vertical window as shown in Fig. The brush weigh 12 N and coefficient of kinetic friction of 0.15. Calculate F (a) 15 N (b) 10.2 N (c) 16.9 N (d) 18.1 N 35. A rock of mass m slides down with an initial velocity v0. A retarding force F = -k v1/2 acts on the body. The velocity at any instant is given by
(a) v = v0 - m kt (b) v = v0 - 2 m kt       (c) m kt v = v0 − (d) None of these 36. At t = 0, a force F kt is applied on a block making an angle  with the horizontal. Suppose surfaces to be smooth. Find the velocity of the body at the time of breaking off the plane. (a)   2a sin mg cos (b)   2 2 2 2a sin m g cos (c)   2 2 2a sin mg cos (d)   2a sin mg cos 2 2 37. A block of mass m is placed on a wedge of mass m and inclination  as shown in Fig. All surfaces are smooth. Find the acceleration of wedge. (a) +   2 2 M msin mg cos (b) +   2 2 M mcos mg sin (c) +    2 M msin mg sin cos (d) +    2 M mcos mg sin cos 38. The tension T in the thread shown in fig is (a) 10 N (b) Zero (c) 98 N (d) 196 N 39. A light spring of spring constant k is cut into two equal halves. Each half is connected in Parallel then net spring constant of the combination is (a) 4 k (b) 2 k (c) 2k (d) 4k 40. A force F = kt( - t) acts on a particle of mass m, which is at rest at t = 0 where k is a constant. Find the momentum of the force when the action of the force is discontinued. (a) 2 k 3  (b) 3 k 3  (c) 6 k 3  (d) 4 k 3  41. The velocity of a bullet changes from v0 to v after the bullet has passed through a distance h in the plank. Assuming resistance offered is proportional to v2 , find the time of motion in the plank. (a) ev v hlog v v t t 0 0 − = (b) t = cv v log v v h 0 0 2 (c) t = ( ) v v v v log v v h 0 0 e 0 − (d) t = ( ) 0 0 vv v − v h 42. A horizontal disc rotates with a constant angular velocity  about a vertical axis passing through its centre. A small body m moves along a diameter with a velocity v. Find the force the disc exerts on the body when it is at a distance r located from the rotation axis. (a) mr 2 + 2mv (b) mg + ( ) 2 2 4 2 m r  + 2mv (c) ( ) 2 2 mv 2 mr 2 m g + 2  +  (d) ( ) 2 2 4 2 m g + r  + 2v 43. A bead A can slide freely along a smooth rod bent in the form of a half circle of Radius R. The system is set in rotation with a constant angular velocity  about a vertical axis OO'. Find the angle  corresponding to steady position of the bead. (a) cos-1          g R 2 (b) cos-1        2 R g (c) sin-1        2 R g (d) cos-1          g R 2 44. A block of mass m is placed on a wedge of mass M. coefficient between then is 