Title 31. Rotational Motion Med 1.pdf ✅

1. In a spinning top, axis moves around the vertical through its point of contact with the ground sweeping out a cone. This movement of the axis of the top around the vertical is known as (a) Rotation (d) Translation (c) Precession (d) Rolling 2. Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (- 1, 3, -2). Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system? (a) (0,0,0) (b) (1,3,2) (c) (-1,2,3) (d) (3,1,8) 3. The position of the centre of mass of a cube of uniform mass density will be at (a) The centre of one face (b) The centre of the interaction of diagonals of one face. (c) The geometric centre of the cube (d) The edge of a cube 4. The reduce mass of two particles having masses m and 2m is (a) 2 m (b) 3 m (c) 3 2m (d) 2 m 5. The x,y coordinates of the centre of mass of a uniform L-shaped lamina of mass 3 kg is (a)       m 6 5 m, 6 5 (b) (1m, 1m) (c)       m 5 6 m, 5 6 (d) (2m, 2m) 6. The centre of mass of a system of two particles of masses m1 and m2 is at a distance dl from m1 and at a distance d2 from mass m2 such that (a) 1 2 2 1 m m d d = (b) 2 1 2 1 m m d d = (c) 1 2 1 2 1 m m m d d + = (d) 1 2 2 2 1 m m m d d + = 7. The centre of mass of a body (a) Lies always at the geometrical centre (b) Lies always inside the body (c) Lies always outside the body (d) May lie within or outside the body 8. When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid air, the centre of mass of the fragments will move (a) Vertically downwards (b) Along the original parabolic path (c) Vertically upwards and then vertically downwards (d) Horizontally followed by parabolic path 9. A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed (a) Zero (b) (v + u) (c) (v – u) (d) v 10. Which of the following is the correct relation between linear velocity v  and angular velocity   of a particle? (a) =     v r (b) v r    =  (c) r v    =  (d) v r    =  11. The direction of the angular velocity vector is along. (a) The tangent to the circular path (b) The inward radius (c) The outward radius (d) The axis of rotation 12. The z component of the angular momentum of a particle whose position vector is r  with components x,y and z and linear momentum is P  with components px , py and pz is (a) xpy – ypx (b) ypz -zpy (c) zpx — xpz (d) xpy + ypx 13. A mass M is moving with a constant velocity parallel to x-axis. Its angular momentum w.r.t. origin (a) Is zero (b) Remains constant (c) Goes on increasing (d) Goes on decreasing 14. Consider a particle of mass m having linear momentum at position relative to the origin O. Let L  be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relates (s) r,p   and L  ? (a) 0 dt dp r dt dL +  =    (b) p 0 dt dp dt dL +  =    (c) p 0 dt dr dt dL +  =    (d) 0 dt dp r dt dL −  =    15. The force k ˆ j 5 ˆ i 3 ˆ 7 + − acts on a particle whose position vector is k ˆ j ˆ i ˆ − + What is the torque of a given force about the origin? (a) k ˆ j 10 ˆ i 12 ˆ 12 + + (b) k ˆ j 12 ˆ i 10 ˆ 2 + + (c) k ˆ j 10 ˆ i 10 ˆ 2 + + (d) k ˆ j ˆ i 2 ˆ 10 + + 16. A couple produces
(a) Purely translational motion (b) Purely rotational motion (c) Both translational and rotational motion (d) No motion 17. When a torque acting upon a system is zero. Which of the following will be constant? (a) Force (b) Linear impulse (c) Linear momentum (d) Angular momentum 18. Which of the following statements is incorrect? (a) A pair of equal and opposite forces with different lines of action is known as couple. (b) A couple produces rotation without translation. (c) When we open the lid of a bottle by turning it, our fingers apply a couple to the lid. (d) Moment of a couple depends on the point about which we take the moment. 19. Moment of couple is called (a) Angular momentum (b) Force (c) Torque (d) Impulse 20. A disc is rotating with angular velocity   about its axis. A force F  acts at a point whose position vector with respect to the axis of rotation is r  . The power associated with the torque due to the force is given by (a) (  )     r F . (b) (  )    r F (c) ( )    r. F (d) ( )    r F 21. The position of a particle is given by k ˆ j ˆ i 2 ˆ r = + −  and its linear momentum is given by . k ˆ j 2 ˆ i 4 ˆ p = 3 + −  Then its angular momentum about the origin is perpendicular to (a) x-axis (b) y-axis (c) z-axis (d) yzplane 22. The velocity of centre of mass of the system remains constant, if the total external force action on the system is. (a) Minimum (b) Maximum (c) Unity (d) Zero 23. If F  is the force acting on a particle having position vector r  and   be the torque of this force about the origin, then (a) r. 0 and F. 0    (b) r. =0 and F.= 0    (c) r. =0 and F. 0    (d) r. 0 and F.= 0    24. A uniform rod of length 1 m and mass 4 kg is supported on two knife-edges placed 10 cm from each end. A 60 N weight is suspended at 30 cm from one end. The reactions at the knife edges is (a) 60 N, 40 N (b) 75 N,25 N (c) 65 N, 35 N (d) 55 N, 45 N 25. A non-uniform bar of weight W and length L is suspended by two strings of negligible weight as shown in figure. The angles made by the strings with the vertical are 1 and 2 respectively. The distance d of the centre of gravity of the bar from its left end is (a)           +  1 1 2 tan tan tan L (b)          +   1 2 1 tan tan tan L (c)          +   1 2 2 tan tan tan L (d)           +  2 1 2 tan tan tan L 26. (1) Centre of gravity of a body is the point at which the weight of the body acts. (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. (3) To evaluate the gravitational field intensity due to any body at an external point,the entire mass of the body can be considered to be concentrated at its centre of gravity. (4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the centre of gravity of the body to the axis.Which one of the following pairs of statements is correct? (a) (l)and(4) (b) (l)and(2) (c) (2) and (3) (d) (3) and (4) 27. A rigid body is said to be in partial equilibrium, when it is in (a) Translational equilibrium only (b) Rotational equilibrium only (c) Either (a) or (b) (d) Neither (a) nor (b) 28. A uniform cube of mass M and side a is placed on a frictionless horizontal surface. A vertical force F is applied to the edge as shown in figure. Match the Column I with Column II. Column I Column II (A) 2 Mg F 4 Mg   (p) Cube will move up. (B) 2 Mg F  (q) Cube will not exhibit motion. (C) F  Mg (r) Cube will begin to rotate and slip at A. (D) 4 Mg F = (s) Normal reaction effectively at a/3 from A, no motion. (a) A - p, B - q, C - s, D – r (b) A - r, B - s, C - q, D – p (c) A - q, B - r, C - p, D – s (d) A - s, B - p, C - r, D – q 29. Which of the following relations is correct?
(a) Mechanical advantage = Load Effort (b) Load arm × Effort = Effort arm × Load (c) Load arm × Load = Effort arm × Effort (d) None of these 30. A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12 cm mark, the stick is found to be balanced at 45 cm. The mass of the metre stick is (a) 56 g (b) 66 g (c) 76 g (d) 86 g 31. A uniform ladder 3 m long weighing 20 kg leans against a frictionless wall. Its foot rest on a rough floor 1m from the wall. The reaction forces of the wall and floor are (a) 25 2 N,203N (b) 50 2 N,203N (c) 203N,25 2 N (d) 203N,50 2 N 32. A rigid rod of length 2L is acted upon by some forces. All forces labelled F have the same magnitude. Which cases have a non-zero net torque acting on the rod about its centre? (a) I and II only (b) II and III only (c) I and III only (d) The net torque is zero in all cases. 33. Analogue of mass in rotational motion is (a) Moment of inertia (b) Torque (c) Radius of gyration (d) Angular momentum 34. A person is standing on a rotating table with metal spheres in his hands. If he withdraws his hands to his chest, then the effect on his angular velocity will be (a) Increase (b) Decrease (c) Remain same (d) Cant say 35. The moment of inertia of a body depends Upon (a) Mass of the body (b) Axis of rotation of the body (c) Shape and size of the body (d) All of these 36. The moment of inertia of a body depends UponThe moment of inertia of a solid sphere of mass M and radius R about a tangent to the sphere is (a) 2 MR 5 2 (b) 2 MR 5 6 (c) 2 MR 5 4 (d) 2 MR 5 7 37. A solid cylinder of mass M and radius R rotates about its axis with angular speed to. Its rotational kinetic energy is (a) 2 2 MR 2 1  (b) MR2 2  (c) 2 2 MR 4 1  (d) 2 2 MR 8 1  38. Match the Coulum I with Column II. Column I Column II (A) For ranslational Equilibrium (p) Mk2 (B) For rotational Equilibrium (q) Angular acceleration (C) Moment of inertial of a body (r) F = 0  (D) Torque is required to produce (s)  = 0  (a) A - p, B - q, C - r, D – s (b) A - q, B - r, C - s, D – p (c) A - r, B - q, C - p, D – s (d) A - r, B - s, C - p, D - q 39. Two masses each of mass M are attached to the end of a rigid massless rod of length L. The moment of inertia of the system about an axis passing centre of mass and perpendicular to its length is (a) 4 ML2 (b) 2 ML2 (c) ML2 (d) ML2 2 40. The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is (a) 2 1 (b) 3 1 (c) 3 1 (d) 2 1 41. With reference to figure of a cube of edge a and mass m, which of the following is the incorrect statement? (O is the centre of the cube) (a) The moment of inertia of cube about z’ is 2 ma I' I 2 z = z + (b) The moment of inertia of cube about z”is I " z 2 ma I" I 2 z = z +
(c) I x =Iy (d) None of these 42. Which of the following has the highest moment of inertia when each of them has the same mass and the same radius? (a) A ring about any of its diameter. (b) A disc about any of its diameter (c) A hollow sphere about any of its diameter. (d) A solid sphere about any of its diameter. 43. A flywheel rotating at 420 rpm slows down at a constant rate of 2 rad s-2 . The time required to stop the flywheel is (a) 22 s (b) 11s (c) 44 s (d) 12 s 44. An athlete throws a discus from rest to a final angular velocityof 15rads-1 in 0.270 s before releasing it. During acceleration, discus moves a circular arc of radius 0.810 m. Acceleration of discus before it is released is (a) 45 m s-2 (b) 182 m s-2 (c) 187 m s-2 (d) 192 m s-2 45. A cord of negligible mass is wound round the rim of a flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord. The work done by the pull when 2 m of the cord is unwound (a) 20 J (b) 25 J (c) 45 J (d) 50 J 46. In the question number 58, if wheel starts from rest, what is the kinetic energy of the wheel when 2 m of the cord is unwound? (a) 20 J (b) 25 J (c) 45 J (d) 50 J 47. The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is (a) 2 2 rads −  (b) 2 4 rads −  (c) 2 6 rads −  (d) 2 8 rads −  48. A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. If the rope is pulled with a force of 30 N, then the angular acceleration produced in the cylinder is (a) 2 15rads − (b) 2 20rads − (c) 2 25rads − (d) 2 30rads − 49. In the question number 62, the linear acceleration of the rope is (a) 2 5ms − (b) 2 10ms − (c) 2 15ms − (d) 2 20ms − 50. A grindstone has a moment of inertia of 6 kg m2 . A constant torque is applied and the grindstone is found to have a speed of 150 rpm, 10 seconds after starting from rest. The torque is (a) 3Nm (b) 3Nm (c) Nm 3  (d) 4Nm 51. To maintain a rotor at a uniform angular speed of 100 rad s-1 , an engine needs to transmit torque of 100 N m. The power of the engine is (a) 10 kW (b) 100 kW (c) 10 MW (d) 100 MW 52. A hollow cylinder of mass M and radius R is rotating about its axis of symmetry and a solid sphere of same mass and radius is rotating about an axis passing through its centre. If torques of equal magnitude are applied to them, then the ratio of angular accelerations produced is (a) 5 2 (b) 2 5 (c) 4 5 (d) 5 4 53. The instantaneous angular position of a point on a rotating wheel is given by the equation . ( ) 3 2  t = 2t −6t The torque on the wheel becomes zero at (a) t = 1 s (b) t = 0.5 s (c) t = 0.25 s (d) t = 2 s 54. A solid cylinder of mass 20 kg and radius 20 cm rotates about its axis with a angular speed 100 rad s -1 . The angular momentum of the cylinder about its axis is (a) 40 Js (b) 400 Js (c) 20 J s (d) 200 J s 55. When a mass is rotating in a plane about a fixed point its angular momentum is directed along (a) The radius (b) The tangent the orbit (c) The line at angle of 45° to the plane of rotation (d) The axis of rotation 56. A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which of the following is true about his kinetic energy K and angular momentum L? (a) Both K and L increase (b) Both K and L remain unchanged (c) K remains constant, I increases (d) K increases but L remains constant 57. Which of the following principles a circus acrobat employs in his performance? (a) Conservation of energy (b) Conservation of linear momentum (c) Conservation of mass (d) Conservation of angular momentum 58. Angular momentum L and rotational kinetic energy KR of a rigid body are related to each other by the relation.(I = moment of inertia) (a) KR = 2IL (b) 2I L K 2 R = (c) L 2I KR = (d) I L K 2 R = 59. Generally the mass of fly wheel is concentrated in its rim. Why? (a) To obtain a strong wheel (b) To obtain stable equilibrium (c) To increase the moment of inertia (d) To decrease the moment of inertia 60. Total angular momentum of a rotating body remains constant, if the net torque acting on the body is