System of Particles and Rotational Motion Mock Test – Class 11 Physics

1. A rigid body has , but about its centre of mass. The body can

2. The value of is

3. A uniform disc of mass and radius has centre-of-mass velocity towards the right. At the same instant, it has angular speed clockwise. The point is on the ground directly below the centre of the disc. Find the angular momentum of the disc about . Take .

4. For a continuous body, the centre-of-mass formula is obtained from the discrete-particle formula by replacing

5. Two vectors have magnitudes and , and the angle between them is . If they are used in the order , the magnitude of the result is

6. Angular momentum of a particle about a point is defined as

7. A wheel is rotating with angular speed but its centre is not moving. This motion is not rolling without slipping on a horizontal surface because

8. A composite body is made by joining two point-replaceable parts. Part P has mass and its own centre at . Part Q has mass and its own centre at . The centre of mass of the composite body is

9. A rigid body rotates with angular speed . A point at distance from the axis has linear speed

10. Study the table and choose the row that correctly connects torque and angular momentum.

11. The expression most naturally denotes

12. A rocket and its fuel are initially treated as one system. After some fuel is expelled, a calculation that considers only the remaining rocket must

13. A two-particle system has masses and at positions and . If both masses are doubled while their positions remain unchanged, will

14. The SI unit of moment of inertia is

15. For particles distributed in three-dimensional space, the -coordinate of the centre of mass is written as

16. A rolling body descends an incline without slipping. If the angle of the incline is increased while the body and surface condition remain suitable for pure rolling, its acceleration

17. For a uniform thin rod along the -axis, the small mass element may be written as , where is constant. This helps because

18. In a variable-mass situation such as a rocket ejecting fuel, the ordinary centre-of-mass formula should be applied carefully because

19. A uniform thin rod of length is placed along a straight line. By symmetry, its centre of mass is located

20. A rigid body rotates about a fixed axis. All particles of the body have the same

21. A -versus- graph for a rotating body is a straight line from to . The work done by the torque is

22. Two rotating bodies have the same angular momentum , but body P has a larger moment of inertia than body Q. Their rotational kinetic energies are compared. The correct statement is

23. Match each situation with the most suitable centre-of-mass idea.

24. A shell moving horizontally explodes into fragments in mid-air. During the short explosion, gravity is the only significant external force. For the horizontal motion of the fragments considered as one system,

25. A disc with moment of inertia rotates at . Its angular momentum about the axis is

26. The SI unit of torque is

27. In the notation used for rotational motion, is introduced as the symbol for

28. A uniform disc has a small circular hole cut out away from its centre. For locating the centre of mass of the remaining lamina, the most suitable modelling step is to

29. Study the table and select the row that correctly compares sliding and rolling from the same height , neglecting losses.

30. A cart contains a block. A horizontal force of acts on the cart-block system as a whole, and friction with the ground is negligible. The acceleration of the centre of mass of the cart-block system is

31. A solid cylinder rolls without slipping down an incline. The frictional force on it acts up the incline. Its role is mainly to

32. The cross product equals

33. Assertion: Angular momentum is conserved when the net external torque about the chosen point is zero.
Reason: A zero net external torque gives .

34. For a body rolling without slipping, using about the instantaneous contact point gives the same total kinetic energy as the translational-plus-rotational form because

35. A wheel of radius rolls without slipping with angular speed . The speed of its centre is

36. A compact data table for a rotating body is shown below. Select the row that is physically suitable.

37. Two particles of masses and are placed at and , respectively. Find .

38. A system has two particles of mass at and , and a third particle of mass at . Its centre of mass is

39. A body is made by joining a small heavy block to one end of a light rod. Compared with the geometrical midpoint of the rod, the centre of mass of the combined body will be shifted

40. Use the arrangement described below. A wheel rolls to the right without slipping on a horizontal road. Point P is the topmost point, point Q is the centre, and point R is the point of contact with the road. The speeds relative to the road are best ordered as

41. The centre of mass of a uniform rectangular lamina lies at

42. A disc rotates about a fixed vertical axis. Two tangential forces and act at the same radius in opposite rotational senses. The net torque magnitude is

43. A non-uniform rod is thicker and heavier near its left end. Its geometrical midpoint and centre of mass are compared. The centre of mass is expected to be

44. A rolling solid cylinder is analysed using the instantaneous contact point as the axis. If , then is

45. A graph of angular acceleration versus torque for a rigid body rotating about a fixed axis is a straight line through the origin. The slope of the graph is

46. A thin ring rolls without slipping with centre-of-mass speed . If , its total kinetic energy is

47. A flywheel starts from rest and has constant angular acceleration . Its angular displacement in is

48. A thin ring rolls without slipping from rest down a vertical height . Its speed at the bottom is

49. Read the case below and answer the question.

The position of the centre of mass is

50. A thin ring and a solid cylinder have the same mass , radius , and angular speed while rolling without slipping. Their total kinetic energies are in the ratio