Systems of Particles & Rotational Motion — 50 MCQs

1. Centre of mass of a uniform semicircular wire of radius R lies at a distance from centre:

A. 0.5 R

B. 2R/π

C. 0.637R

D. R

Answer: C

2. Total external force on a system of particles equals M a_cm where M is total mass and a_cm is acceleration of:

A. Any particle

B. Centre of mass

C. Heaviest particle

D. Fixed origin

Answer: B

3. Linear momentum of a system of particles is constant if:

A. Internal forces non-zero

B. External force is zero

C. Centre of mass fixed

D. Mass changes

Answer: B

4. Impulse delivered by force F over time Δt equals:

A. F/Δt

B. ∫F dt

C. F·Δt only if F constant

D. Both B and C

Answer: D

5. Angular momentum L of a particle about a point is defined as:

A. r × p

B. p × r

C. r · p

D. p / r

Answer: A

6. Torque τ about an axis equals rate of change of:

A. Linear momentum

B. Angular momentum

C. Kinetic energy

D. Potential energy

Answer: B

7. Moment of inertia of a point mass m at distance r from axis is:

A. m/r

B. m r^2

C. mr

D. m r^3

Answer: B

8. Parallel-axis theorem relates I_about new axis to I_about CM by adding:

A. M d

B. M d^2

C. m d^2/2

D. Zero

Answer: B

9. Rotational kinetic energy of rigid body =

A. 1/2 I ω

B. 1/2 I ω^2

C. I ω^2

D. I ω

Answer: B

10. For rolling without slipping v_cm and angular speed ω relate as:

A. v_cm = ω / R

B. v_cm = R ω

C. v_cm = R / ω

D. v_cm = ω^2 R

Answer: B

11. If net external torque on system is zero, total angular momentum about that axis is:

A. Increasing

B. Conserved

C. Decreasing

D. Zero

Answer: B

12. Unit of moment of inertia is:

A. kg·m

B. kg·m^2

C. N·m

D. J·s

Answer: B

13. A uniform rod of length L about its centre has I = (1/12) m L^2. Moment about one end is:

A. (1/12) m L^2

B. (1/3) m L^2

C. (1/4) m L^2

D. (1/2) m L^2

Answer: B

14. For small oscillations, a physical pendulum has period T = 2π √(I/(m g d)). Here d is distance from pivot to:

A. Centre of mass

B. Pivot to end

C. Support

D. Any point

Answer: A

15. Angular impulse equals change in:

A. Linear momentum

B. Angular momentum

C. Kinetic energy

D. Potential energy

Answer: B

16. A ring and a solid disk of same mass and radius roll down same incline without slipping. Which reaches bottom first?

A. Ring

B. Disk

C. Both same

D. Depends on incline

Answer: B

17. Angular momentum of particle m moving with velocity v at perpendicular distance r from origin is L =:

A. m v / r

B. m v r

C. m v r^2

D. v r / m

Answer: B

18. Gyroscope resists change in orientation because of:

A. High moment of inertia

B. Angular momentum and its conservation

C. Friction only

D. Gravity only

Answer: B

19. Rotational analogue of F = ma is:

A. τ = I α

B. τ = m a

C. L = I ω

D. τ = L / t

Answer: A

20. If a rigid body rotates about fixed axis, each particle undergoes:

A. Pure translation

B. Pure rotation about axis

C. Random motion

D. No motion

Answer: B

21. For a rigid body, total kinetic energy = translational KE of CM + rotational KE about CM. True or false?

A. True

B. False

C. Only for point masses

D. Only for symmetric bodies

Answer: A

22. A system of particles exerts only internal forces. Total momentum of system:

A. Changes

B. Remains constant

C. Becomes zero

D. Doubles

Answer: B

23. Moment of inertia of solid cylinder about central axis is:

A. 1/2 m R^2

B. 1/4 m R^2

C. m R^2

D. 2/3 m R^2

Answer: A

24. A particle of mass m moves in circle of radius r with angular speed ω. Its kinetic energy is:

A. 1/2 m r^2 ω

B. 1/2 m r^2 ω^2

C. m r^2 ω^2

D. 1/2 m ω^2

Answer: B

25. Which of following has largest moment of inertia about central axis (same mass, same outer radius)?

A. Solid disk

B. Thin ring

C. Solid sphere

D. Hollow sphere

Answer: B

26. If angular speed of a rotating body is doubled, its rotational KE becomes:

A. Twice

B. Four times

C. Half

D. Unchanged

Answer: B

27. A wheel spinning freely in space has zero external torque. Its angular momentum will:

A. Increase

B. Remain constant

C. Decrease

D. Oscillate

Answer: B

28. Rolling without slipping implies point of contact has instantaneous velocity:

A. v_cm

B. ωR

C. Zero

D. 2 v_cm

Answer: C

29. For a system of particles, internal torques about CM are:

A. Add up to net external torque

B. Cancel pairwise

C. Always zero individually

D. Infinite

Answer: B

30. A hollow cylinder and solid cylinder (same mass, radius) have moments I_hollow = mR^2, I_solid = 1/2 mR^2. Which requires more torque to achieve same α?

A. Solid cylinder

B. Hollow cylinder

C. Both same

D. Depends on mass

Answer: B

31. Angular velocity ω is related to linear velocity v by v = ω r. Units of ω are:

A. rad/s

B. m/s

C. s

D. None

Answer: A

32. Conservation of angular momentum explains why a figure skater spins faster when:

A. She extends arms

B. She pulls arms in

C. Throws mass outward

D. Jumps

Answer: B

33. If a torque τ acts for time Δt, angular impulse equals:

A. τ/Δt

B. τ Δt

C. τ + Δt

D. τ − Δt

Answer: B

34. Angular momentum of rigid body can be written as L = I ω if axis is:

A. Principal axis through CM

B. Any axis

C. Parallel to velocity

D. Perpendicular to plane

Answer: A

35. Work done to spin a rigid body from rest to angular speed ω is:

A. 1/2 I ω

B. 1/2 I ω^2

C. I ω^2

D. I ω

Answer: B

36. A disk and a hoop both of same mass and radius have same angular speed. Which has larger rotational KE?

A. Disk

B. Hoop

C. Same

D. Depends on ω

Answer: B

37. A particle moves radially outward on frictionless turntable conserving angular momentum. Its angular speed:

A. Increases

B. Decreases

C. Unchanged

D. Zero

Answer: B

38. Torque due to force F applied at position r is τ = r × F. If r parallel F, τ is:

A. Maximum

B. Zero

C. r F

D. r / F

Answer: B

39. Rotational motion about fixed axis: equation τ_net = I α assumes I is constant. True when:

A. Mass distribution changes

B. Axis fixed in body

C. Axis fixed in space and body rigid

D. Body deforming

Answer: C

40. A wheel of radius R rolls without slipping with velocity v. Point on rim instantaneously at top has speed relative ground:

A. v

B. 0

C. 2v

D. v/2

Answer: C

41. A system's centre of mass moves as if all external forces act on a single particle of mass M located at CM. This is:

A. Newton's second law for a system

B. Conservation of energy

C. Definition of torque

D. Parallel-axis theorem

Answer: A

42. For small oscillations of physical pendulum, period depends on:

A. Mass only

B. Moment of inertia about pivot and distance to CM

C. Amplitude

D. Friction only

Answer: B

43. If two particles of masses m and 2m located at x=0 and x=L respectively, centre of mass is at x =

A. L/3

B. 2L/3

C. L/2

D. 3L/4

Answer: B

44. A flywheel stores energy primarily as:

A. Potential energy

B. Rotational kinetic energy

C. Thermal energy

D. Chemical energy

Answer: B

45. When two particles collide and stick, about which quantity is conserved (if no external force)?

A. Kinetic energy

B. Linear momentum

C. Angular momentum only

D. Both A and B

Answer: B

46. If mass distribution moves closer to axis while conserving angular momentum, angular speed:

A. Decreases

B. Increases

C. Unchanged

D. Zero

Answer: B

47. A torque applied perpendicular to plane of rotation causes:

A. Change in magnitude of angular velocity only

B. Change in direction of angular momentum only

C. Change in angular momentum (magnitude and/or direction)

D. No effect

Answer: C

48. For small amplitude rotational oscillations, restoring torque τ ≈ −k θ. Angular frequency ω is:

A. √(k/I)

B. k/I

C. I/k

D. √(I/k)

Answer: A

49. A particle of mass m moving in straight line at distance b from pivot has angular momentum L = m v b. If b=0, L =

A. m v

B. Zero

C. Infinity

D. m v / b

Answer: B

50. A rigid body free in space rotates about its centre of mass. Is CM motion required for rotation?

A. Yes, CM must move

B. No, rotation can occur about CM while CM at rest

C. Only if external forces act

D. Only for asymmetric bodies

Answer: B