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

1. A rotating disc has angular speed . Point P is at radius , and point Q is at radius . The ratio of their linear speeds is

2. Use the graph description below.

The slope of the graph represents

3. A rotating ceiling fan is considered a rigid body in elementary rotational motion because

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

5. In the component method for a many-particle system, is found using

6. A rigid body rolls without slipping with . If its centre has acceleration but the angular acceleration is not equal to , the motion

7. In a uniform gravitational field, the centre of gravity and centre of mass of a rigid body

8. A crate of height and base length rests on the floor of a truck. The base length is along the direction of motion. The truck accelerates horizontally towards the right. The coefficient of static friction between the crate and the truck floor is , and . Assuming the crate has uniform density, what happens first as the truck acceleration is slowly increased?

9. A force of acts on a body. The perpendicular distance from the chosen axis to the force's line of action is . The torque magnitude about that axis is

10. Consider the following statements about rolling without slipping.
I. The point of contact is instantaneously at rest relative to the ground.
II. The condition holds.
III. The top point of the rolling wheel has zero speed relative to the ground.

11. A variable-mass caution is most closely connected with the idea that

12. A student tries to use the perpendicular-axis theorem for a solid cylinder about three mutually perpendicular axes through its centre. The main problem with this method is that

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

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

15. Moment of inertia of a rigid body about a given axis measures

16. A table of values is prepared for finding of several particles.

The row that contains an unsuitable method is

17. Pure rolling without slipping of a wheel on a horizontal surface requires the contact point to have

18. A solid sphere rolls without slipping down an incline. The minimum coefficient of static friction needed for pure rolling is found by comparing the required friction with the normal reaction. If , then the required friction is

19. A thin ring rolling without slipping down an incline has acceleration

20. Study the table and select the row with the correct unit-vector cross product.

21. Moment of inertia is larger when more mass is placed farther from the axis mainly because

22. Study the table and choose the row that correctly describes angular momentum about a chosen origin.

23. A particle has position vector and momentum . Its angular momentum about the origin is

24. Three particles of masses , , and are placed at , , and , respectively. Find .

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

26. A force produces clockwise rotation about a fixed axis. If anticlockwise torque is taken as positive, the torque of this force is

27. Read the case below and answer the question.

The centre of mass is located

28. The torque of a couple is independent of the chosen origin because

29. For a solid sphere rolling without slipping down an incline, the minimum coefficient of static friction required is

30. A solid sphere rolls without slipping with speed . Given , its total kinetic energy is

31. Consider the following statements about centre of mass.
I. It depends on the distribution of mass in the system.
II. It must always lie inside the material body.
III. It may represent the translational motion of the system.

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

33. A coordinate axis is shifted to the right. The coordinates of two fixed particles change, and the numerical value of also changes. What remains unchanged?

34. 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 ?

35. A uniform rod extends from to . Using , the centre of mass is

36. A wheel rolls without slipping. If its angular speed is doubled while its radius remains unchanged, the centre-of-mass speed

37. Two particles of masses and move along the -axis with velocities and , respectively. The velocity of the centre of mass is

38. A rigid body is best idealised as a body in which

39. A body of mass moving at catches and sticks to a body of mass initially at rest on a smooth horizontal surface. Immediately after sticking, the velocity of the centre of mass of the combined system is

40. Two unequal masses are placed at the ends of a light rod of length . If is at the left end and is at the right end with , the centre of mass lies

41. A solid sphere rolls without slipping down an incline while a frictionless block slides down the same incline from rest. Neglect air resistance. The block has greater acceleration because

42. A uniform rod of length is made by joining two uniform rods along the same line: one has length and mass , and the other has length and mass . The rods are joined end to end, with the shorter rod on the left. Measured from the left end, the centre of mass is

43. A object moving at breaks into two parts of masses and . The part continues forward at . The speed of the part is

44. In a two-object system, one object is much heavier than the other. The centre of mass lies closer to the heavier object because

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

46. Use the arrangement described below. A vector points out of the page, and a vector points toward the right in the page. Taking right as , upward as , and out of the page as , the direction of is

47. The relation between total momentum and centre-of-mass velocity is

48. A solid cylinder is placed on a rough horizontal surface and pulled horizontally by a string wound around its top, so that it rolls without slipping to the right. The direction of static friction may be different from a cylinder rolling freely down an incline because

49. 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

50. Consider the following statements for a many-particle system.
I. is the total mass of the chosen system.
II. has the same unit as .
III. The largest mass alone always gives the exact centre-of-mass position.