TOPIC : Rotational motion Date : Marks : 120 mks Time : ½ hr 1. A shell (at rest) explodes in to smalll fragment. The C.M. of mass of fragment will move with: a) zero velocity b) constantt velocity c) infinite velocity d) constant velocity double the 2. In case of bodies of regular shapes a) mass b) equilibrium c) 3. A body is in rotational equilibrium means, necessarily: a) It has only zero angular speed c) no torque is acting on the body the entre of gravity coincides with the centre of geometry of body d) both a' and 'c' b) it has zero angular momentum d) maximum torque is acting on the body 4. Angular impulse is a) torque / time b) torque time c) 1 2 torque time d) torque time 2 5. Angular acceleration of a body of mass 50 kg under the action of torque of magnitude 500 Nm is 25 rad/s 2. Then radius of gyration of the body about its axis of rotation is nearly equal to a) 0.2 m b) 0.6 m c) 0.4m d) 1 m 6. A system consists of four particles 1, 2, 3 and 4 gram with their co-ordinate respectively at (2, - 3,+ 1), (1, 2, 3) (4, +2, -1) and (2, 2, -1) then the centre of mass of such a system is at co-ordinates of: a) (0, 12/5,3/2) b) (12/5, 3/2, 0) c) (1,5/12,2/3) d) (5/12,2/3,0) 7. To have a M.I. of rod (thin uniform) about a transverse axis about 10-2 kgm 2 its length should be about (Given mass m = 3 kg) a) 15cm b) 20 cm c) 25cm d) 2 cm 8. The M.I. of a ring of mass M and radius R about an axis passing through its centre and perpendicular to its plane is a) MR 2 /2 b) 3/2 MR 2 c) MR 2 d) 2MR 2 9. A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is (a) (b) (c) (d) 10. A pan containing a layer of uniform thickness of ice is placed on a circular turntable with its centre coinciding with the centre of the turntable. The turntable is now rotated at a constant angular velocity about a vertical axis passing through its centre and driving torque is withdrawn. There is no friction between the table and pivot. As ice metals a) The angular velocity decreases b) The angular velocity increases Page 1 of 5
c) The angular velocity remains unchanged d) The moment of inertia remains unchanged 11. With the increase in temperature, moment of inertia of a solid sphere about the diameter: a) Decrease b) Increases c) Does not change d) Cannot be predicted 12. A solid sphere and a disc of equal radii are rolling on a inclined plane without slipping. One reaches earlier than the other due to different a) sizes b) frictional force c) moment of inertia d) radius of gyration 13. Two circular iron discs are of the same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is a) twice as large b) four times as large c) sixteen times as large d) eight times of large 14. Three particles each of 'm' are kept at the three vertices of an equilateral triangle of side' a,' Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is a) 3ma 2 b) ma 2 c) ma 2 /3 d) 2/3 ma 2 15. A body rolls down an inclined plane If its kinetic energy of rotational motion is 40% of its kinetic energy of translational then the body is a) disc b) hollow sphere c) ring d) solid sphere 16. A point at which -the whole mass of the body is supposed to be concentrated in order to study the motion of an external force in accordance with Newton's laws of motion is a) centre of gravity b) weight of the body c) centre of mass of a body d) acceleration due to gravity acts on a body 17. A mass attached to massless spring is whirled in a circular path with constant angular velocity and its angular momentum is L. If the spring is halved keeping the velocity same the angular momentum is : a) L/4 b) L c) 2L d) L/2 18. The M.I. of disc of mass M and radius 'R' about an axis passing through midway between centre and circumference and perpendicular to its plane is a) MR2/2 b) 5/4 MR2 c) MR2 d) 3/4 MR2 19. A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque on the ring, it stops after making n revolutions. After how many revolutions will the disc stop, if the retarding torque of it is also? a) b) n c) 2n d) 4n 20. When a polar ice caps melt, then the duration of day a) increases b) decreases c) sometimes decreases, sometimes increases d) remains constant Page 2 of 5
21. A torque of magnitude 400 Nm acting on a body of mass 4 kg which produces an acceleration of 20 rad/s 2. The radius of gyration about that axis is: a) 70 m b) 22.36 m c) 2.26 m d) 0.8 m 22. If earth we suddenly condensed to 40 % of the present radius without change of mass the length of the day will be : a) 38.4 Hrs. b) 20 Hrs. c) 3.84 Hrs d) 60 Hrs. 23. The M.I. of thin uniform rod of masss 'M' and length, l about an axis passing through its one end and, perpendicular to length is a) Ml 2 b) M l 2 / 3 c) MI l 2 / 2 d) MI l / 12 24. A body moves with constant velocity parallel to X-axis. Its angular momentum with respect to origin a) is zero b) remains constant c) goes on increasing d) goes on decreasing 25. The angular momentum and the moment of inertia are respectively a) vector and tensor quantities b) scalar and vector quantities c) vector and vector quantities d) scalar and scalar quantities 26. When mass is rotating in a plane about a fixed point. Its angular momentum is directed along: a) The radius b) The tangent to orbit c) Line at angle of 45 to the plane of rotation d) The axis of rotation 27. The radius of gyration of a solid sphere about a tangent in its plane is given by a) 2/3 b) 5/3R c) 2/5R d) 7/5R 28. Two particles of mass 2 kg and 2.5 kg moves with a velocity of 15 m/sec and 35m/sec. The velocity of their centre of mass moves with speed of: a) 2.5 m/sec b) 26.11 m/ /sec c) 2.61 m/sec d) 20 m/sec 29. If all of a sudden the radius of the earth increases then (Assume earth as a sphere) : a) The angular momentum of earth will become greater than that of previous b) The orbital speed of the earth willl increase c) The periodic time of the earth will increase d) K.E. of earth will remain constant 30. With the increase n temperature, moment of inertia of a solid sphere about the diameter. a) Decreases b) Increases c) Does not change d) None of these 3 P a g e
ANSWERS 1. (b) 2. (d) 3. (c) 4. 11. (b) 12. (d) 13. (c) 14. 21. (c) 22. (a) 23. (b) 24. (b) 5. (b) 6. (b) 7. (b) 8. (c) 9. (b) 10. (a) (b) 15. (d) 16. (c) 17. (a) 18. (a) 19. (b) 20. (a) (b) 25. (a) 26. (d) 27. (d) 28. (b) 29. (c) 30. (b) Solutions 5. 6. 7. 10. 15. 17. 21. 22. Page 4 of 5
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