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

1. If an isolated system has total momentum , its centre of mass

2. A point on a rotating wheel is from the axis. If the angular acceleration is , the tangential acceleration of the point is

3. Consider the following statements about .
I. The formula uses the position vector of every particle in the chosen system.
II. The total mass is a scalar.
III. The formula is valid only when all particles lie on a straight line.

4. 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.

5. A particle is at , and a particle is at . The centre of mass of the two-particle system is

6. A firecracker initially at rest explodes into two fragments on a smooth horizontal surface. During the short explosion, horizontal external force is negligible. The centre of mass

7. 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?

8. If units, units, and the angle between and is , then is

9. The total linear momentum of a system of particles is written as

10. A wheel rolls to the right without slipping. At a point on the rim directly in front of the centre, the rotational velocity relative to the centre is

11. 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

12. Consider the following statements about recoil and explosion examples.
I. They are commonly analysed by choosing a system that includes all separating parts.
II. Momentum conservation can hold even though kinetic energy may change.
III. Momentum conservation requires every fragment to move with equal speed.

13. 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

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

15. The value of is

16. A statement says, "The centre of mass of a body is always the same as its geometrical centre." The best evaluation of this statement is that it is

17. A system has a centre-of-mass acceleration of toward the west. The net external force on the system is

18. A solid cylinder and a hollow cylinder have the same mass and radius and rotate with the same angular speed about their central axes. The hollow cylinder has greater rotational kinetic energy because

19. A plane lamina lies in the -plane. If about two perpendicular axes in its plane through the same point, and about the perpendicular axis through that point, then is

20. The expression is mainly used when the mass distribution is

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

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

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

24. A solid cylinder and a thin ring have the same mass, radius, and centre-of-mass speed while rolling without slipping. The ratio of rotational kinetic energy of the cylinder to that of the ring is

25. Use the graph description below.

What does the slope of this graph represent?

26. 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

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

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

29. A thin ring and a solid sphere roll without slipping down the same incline from rest. Which reaches the bottom first, neglecting air resistance?

30. A thin ring rolling without slipping down an incline requires what minimum coefficient of static friction?

31. The condition for translational equilibrium of a rigid body is

32. A vector product is chosen instead of a scalar product when the required physical quantity must

33. For three particles of masses , , and included in one system, what is the total mass ?

34. Use the arrangement described below. A vector points along , and a vector points along . The direction of is

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

36. Study the table and identify the row that misuses conservation of linear momentum.

37. Read the case and answer the question.

How does the centre of mass shift after the third ball is added?

38. A vector lies in the plane of a page toward the right, and lies in the same plane upward. The direction of is

39. A laboratory record gives the following data for a rotating body: , , and . The instantaneous power delivered by the net torque is

40. A body rolls without slipping from rest down a height . If its value of in is , the speed formula reduces to

41. Two particles inside a system exert equal and opposite forces on each other along the same line. In the equation for the whole system, these two forces

42. A thin ring and a uniform disc have the same mass and radius . Their moments of inertia about central axes perpendicular to their planes are compared. The difference is

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

44. 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

45. The cross product equals

46. A uniform beam of length and weight is supported at its left end. A vertical upward force is applied at the right end to keep the beam horizontal. Neglecting other supports, the upward force must be

47. Consider the following statements about centre of mass by symmetry.
I. A uniform solid sphere has its centre of mass at its centre.
II. A uniform circular disc has its centre of mass at its centre.
III. A uniform ring cannot have its centre of mass at an empty point.

48. A object moving at breaks into two parts. One part of mass moves backward at . The speed of the other part is

49. Consider the following statements about composite-body centre-of-mass calculations.
I. Each simple part may be replaced by its mass placed at its own centre of mass.
II. The coordinate origin can be chosen for convenience, but all part coordinates must then use the same origin.
III. Removed material is treated as positive mass at the centre of the removed part.

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