NEET UG - Rigid body rotation and equations of rotational motion, comparison of linear and rotational motions Online Test (MCQ Quiz)

1. What is the primary characteristic of a rigid body?

A) It deforms significantly under applied forces. B) Its constituent particles maintain fixed relative positions. C) It is always in a state of rest. D) It is always in a state of uniform motion.

2. Which physical quantity represents the tendency of a force to rotate an object around an axis?

A) Linear momentum B) Torque C) Angular momentum D) Impulse

3. The SI unit of torque is:

A) Newton-meter (N m) B) Joule (J) C) Pascal (Pa) D) Watt (W)

4. What is the rotational analogue of linear velocity?

A) Angular acceleration B) Angular displacement C) Angular velocity D) Linear acceleration

5. Which equation describes the relationship between torque and angular acceleration for a rigid body?

A) τ = Iα B) τ = mr C) τ = Fd D) τ = mv

6. The rotational analogue of mass is:

A) Moment of inertia B) Angular momentum C) Torque D) Angular velocity

7. What does the moment of inertia depend on?

A) Mass and distribution of mass from the axis of rotation B) Only the mass of the body C) Only the speed of rotation D) The applied force

8. If a rigid body is rotating with constant angular velocity, what is its angular acceleration?

A) Non-zero B) Zero C) Infinite D) Depends on the mass

9. Which of the following equations is a rotational kinematic equation analogous to v = u + at?

A) ω = ω₀ + αt B) ω = ω₀t + ½αt² C) ω² = ω₀² + 2αθ D) θ = ω₀t + ½αt²

10. The rotational analogue of linear displacement is:

A) Angular velocity B) Angular acceleration C) Angular displacement D) Torque

11. Which equation is analogous to s = ut + ½at² for rotational motion?

A) θ = ω₀t + ½αt² B) ω = ω₀t + ½αt² C) θ = ωt + ½αt² D) s = ω₀t + ½αt²

12. The rotational analogue of linear momentum (p = mv) is:

A) Angular momentum (L = Iω) B) Torque (τ = Iα) C) Angular velocity (ω) D) Moment of inertia (I)

13. For a rigid body rotating about a fixed axis, the rate of change of angular momentum is equal to:

A) The net external torque B) The moment of inertia C) The angular acceleration D) The angular velocity

14. If no net external torque acts on a rotating rigid body, its:

A) Angular momentum changes B) Angular momentum remains constant C) Angular velocity becomes zero D) Moment of inertia changes

15. Which equation is analogous to v² = u² + 2as for rotational motion?

A) ω² = ω₀² + 2αθ B) v² = ω₀² + 2αθ C) ω² = u² + 2αθ D) ω² = ω₀² + 2as

16. The work done by a torque τ acting through an angular displacement θ is:

A) W = τθ B) W = τ/θ C) W = τ + θ D) W = τ - θ

17. The rotational analogue of kinetic energy (½mv²) is:

A) Rotational kinetic energy (½Iω²) B) Linear kinetic energy (½mv²) C) Potential energy D) Work done

18. If a body is rotating and translating simultaneously, its total kinetic energy is:

A) Sum of translational and rotational kinetic energies B) Only translational kinetic energy C) Only rotational kinetic energy D) Product of translational and rotational kinetic energies

19. The condition for rolling without slipping involves a relationship between linear velocity and angular velocity. This relationship is:

A) v = Rω B) v = R/ω C) v = ω/R D) v = R²ω

20. In rotational motion, the quantity that measures the resistance to change in rotational motion is:

A) Moment of inertia B) Torque C) Angular momentum D) Angular velocity

21. What is the SI unit of angular velocity?

A) Radians per second (rad/s) B) Radians per meter (rad/m) C) Meters per second (m/s) D) Radians per second squared (rad/s²)

22. What is the SI unit of angular acceleration?

A) Radians per second squared (rad/s²) B) Radians per second (rad/s) C) Radians D) Radians per meter squared (rad/m²)

23. Which of the following is NOT a vector quantity in rotational motion?

A) Angular velocity B) Angular acceleration C) Torque D) Angular displacement (for finite angles)

24. The direction of angular velocity vector is typically determined by:

A) The right-hand rule B) The left-hand rule C) Newton's first law D) The direction of the applied force

25. For a point mass m rotating at a distance r from the axis of rotation, its moment of inertia is:

A) mr² B) m/r C) mr D) m²r

26. Which statement best describes the relationship between linear and rotational motion?

A) They are independent phenomena. B) Rotational motion is the cause of linear motion. C) Linear motion is the cause of rotational motion. D) They are analogous concepts with corresponding quantities and laws.

27. Consider a solid cylinder rotating about its central axis. Its moment of inertia is given by:

A) ½MR² B) MR² C) ²/₃MR² D) ¹/₁₂M(L²+R²)

28. Consider a thin rod rotating about its center. Its moment of inertia is given by:

A) ¹/₁₂ML² B) ML² C) ½ML² D) ²/₃ML²

29. The parallel axis theorem states that the moment of inertia about an axis parallel to a diameter is:

A) I = I_cm + Md² B) I = I_cm - Md² C) I = I_cm * Md² D) I = I_cm / Md²

30. If a force F acts at a perpendicular distance r from the pivot point, the magnitude of the torque is:

A) Fr B) F/r C) F+r D) F-r

31. Which quantity is conserved in the absence of external torque for a rigid body?

A) Angular momentum B) Angular velocity C) Moment of inertia D) Rotational kinetic energy

32. The rate of change of linear velocity is linear acceleration. The rate of change of angular velocity is:

A) Angular acceleration B) Angular momentum C) Torque D) Angular displacement

33. If a rigid body is rotating and its moment of inertia decreases, what happens to its angular velocity if angular momentum is conserved?

A) Increases B) Decreases C) Remains constant D) Becomes zero

34. The product of moment of inertia and angular velocity is:

A) Angular momentum B) Angular acceleration C) Torque D) Rotational kinetic energy

35. Which equation correctly relates the angular impulse to the change in angular momentum?

A) ∫τ dt = ΔL B) ∫τ dt = Δω C) ∫τ dt = ΔI D) ∫τ dt = Δθ

36. Consider a hoop rotating about its central axis. Its moment of inertia is:

A) MR² B) ½MR² C) ²/₃MR² D) ¹/₂M(R₁²+R₂²)

37. The angular displacement is related to linear displacement for a point on a rotating object by:

A) s = rθ B) s = r/θ C) s = θ/r D) s = r²θ

38. What is the rotational analogue of force?

A) Torque B) Moment of inertia C) Angular momentum D) Angular acceleration

39. If a rigid body is rotating, its constituent particles have:

A) Tangential velocity and centripetal acceleration B) Only radial velocity and tangential acceleration C) Only tangential acceleration D) No velocity or acceleration

40. The rotational kinematic equations are valid when:

A) Angular acceleration is constant B) Angular velocity is constant C) Torque is zero D) Moment of inertia is zero

41. Which of the following is a scalar quantity?

A) Angular displacement (for finite angles) B) Angular velocity C) Angular acceleration D) Torque

42. The center of mass of a rigid body is the point where:

A) The entire mass of the body can be assumed to be concentrated for translational motion. B) The body always remains at rest. C) The rotational motion originates. D) The net force is always zero.

43. For a rigid body undergoing pure rotation about a fixed axis, the velocity of any particle is:

A) Perpendicular to the radius vector from the axis of rotation. B) Parallel to the radius vector from the axis of rotation. C) Along the axis of rotation. D) Zero.

44. The angular position of a point on a rotating body can be measured in:

A) Radians or degrees B) Meters or feet C) Seconds or minutes D) Newtons or pounds

45. If the net torque on a rigid body is zero, then:

A) The angular momentum is constant. B) The angular acceleration is constant. C) The moment of inertia is constant. D) The angular velocity is zero.

46. Which statement is incorrect regarding rigid body rotation?

A) All points on a rigid body rotate through the same angular displacement in a given time. B) All points on a rigid body rotate through the same angular velocity. C) All points on a rigid body rotate through the same angular acceleration. D) The linear velocity of points on a rigid body depends on their distance from the axis of rotation.

47. The rotational analogue of Newton's second law (F=ma) is:

A) τ = Iα B) L = Iω C) τ = dL/dt D) F = ma

48. Which of the following is a condition for equilibrium of a rigid body?

A) Net external force is zero AND net external torque is zero. B) Net external force is zero. C) Net external torque is zero. D) Net linear momentum is conserved.

49. The rotational analogue of impulse (FΔt) is:

A) Angular impulse (τΔt) B) Torque (τ) C) Angular momentum (L) D) Moment of inertia (I)

Rigid body rotation and equations of rotational motion, comparison of linear and rotational motions - Online Test

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