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

1. For two particles, the total angular momentum about the origin is

2. A compact summary of pure rolling is shown below. Select the unsuitable row.

3. A body with rolls without slipping down an incline. The minimum coefficient of static friction required is

4. A rolling body has . For the same centre-of-mass speed , its total kinetic energy can be written as

5. A body rolling without slipping climbs a rough inclined plane and slows down. The rolling condition during the motion is

6. 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

7. A solid cylinder of mass and radius rests on a rough horizontal floor. A light string is wound around the cylinder and pulled horizontally towards the right from the topmost point with a force of . The cylinder rolls without slipping. If and , find the acceleration of the centre and the minimum coefficient of static friction required.

8. Consider the following statements about a rigid body in equilibrium.
I. prevents translational acceleration.
II. prevents angular acceleration.
III. alone always guarantees complete equilibrium.

9. Three particles of masses , , and are at perpendicular distances , , and , respectively, from a fixed axis. The moment of inertia of the system about the axis is

10. A compact way to describe the transition from a discrete system to a continuous body is

11. Internal torques in a system of particles cancel in the total angular momentum equation when the internal forces are central because

12. A uniform beam of length and mass is supported at , the left end, and at , a point from . A load is placed at the right end of the beam. The support at can exert a vertical force either upward or downward, while the support at exerts an upward force. If , what are the vertical reactions at and ?

13. The magnitude of the vector product is

14. For a system of many particles, the vector expression for the centre of mass is

15. Assertion: For two positive masses on a line, the centre of mass lies between the two particle positions.
Reason: is a weighted average of the two coordinates with positive weights.

16. In pure rolling on a rough horizontal surface, static friction may be present. For a wheel rolling steadily without slipping, the instantaneous point of contact has zero velocity relative to the ground. This means static friction

17. A hollow uniform spherical shell and a solid uniform sphere have the same outer centre. For each body considered separately, the centre of mass is at the common centre because

18. A uniform square lamina of side has a square of side removed from its upper-right corner. Take the centre of the original square as origin, with axes parallel to its sides. The centre of the removed square is at . If the full square has mass , the centre of mass of the remaining lamina is

19. A wheel rolls to the right without slipping. At the topmost point of the wheel, the speed relative to the ground is

20. A solid cylinder rolls without slipping down an incline of angle . Taking , its acceleration is

21. 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

22. Take as east, as north, and as upward. If points east and points north, the torque points

23. A system has non-zero total momentum. This necessarily means that

24. In a two-dimensional torque problem, a positive torque is usually assigned to anticlockwise rotation. This sign convention is useful because it

25. Newton's second law for a system of particles is most generally written as

26. A wheel of radius rolls without slipping. Its centre has acceleration . The angular acceleration of the wheel is

27. 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

28. A force acts at a distance from a pivot. If the angle between and is changed from to while and remain fixed, the torque magnitude becomes

29. If is doubled, is tripled, and the angle between them remains unchanged, then becomes

30. Take east as , north as , and upward as . The direction of is

31. A body moves so that every line drawn inside it remains parallel to its initial direction throughout the motion. This observation mainly indicates

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

33. A uniform lamina is made by joining a square plate of mass with a smaller square plate of mass along one side. Their individual centres lie on the same horizontal line and are separated by . Measured from the centre of the larger square toward the smaller square, the centre of mass is

34. A system of two blocks is pulled horizontally by an external force of . The blocks have masses and . Ignoring friction, the acceleration of the centre of mass is

35. A uniform rod of length has its left half made of material with mass and its right half made of material with mass . The centre of mass from the left end is

36. In a uniform metre scale balanced at its centre, the weight of the scale itself produces no torque about the support because

37. A uniform circular ring is lying in a plane. Its centre of mass is at the geometrical centre because

38. A force acts at a point whose position vector from the origin is . The torque about the origin is

39. Which idea is closest to the basic meaning of centre of mass?

40. For a rolling body descending an incline, the formula shows that the acceleration is independent of

41. Two particles of masses and are separated by . A claim says, "The centre of mass is almost at the particle, so the lighter particle can be ignored completely." The best response is that the claim is

42. In the vector formula , shifting every particle by the same displacement vector changes the centre-of-mass position vector by

43. A skater spinning with arms extended pulls the arms close to the body. Neglecting external torque, the skater spins faster mainly because

44. The angular momentum of a rigid body rotating about a fixed symmetry axis is written as

45. The rotational form of Newton's second law for a rigid body rotating about a fixed axis is

46. The angular momentum of a system of particles about a point is found by

47. A point on a rotating body has centripetal acceleration

48. Read the situation below and answer the question.

What can be concluded about the system's angular momentum about the vertical axis?

49. For a rolling body descending without slipping, the fraction of its total kinetic energy that is rotational is

50. A thin ring and a solid sphere roll without slipping from the same height . The body with larger speed at the bottom is