NEET UG - Moment of a force, torque, angular momentum, conservation of angular momentum and applications Online Test (MCQ Quiz)

1. What is the SI unit of torque?

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

2. Torque is defined as the product of:

A) Force and perpendicular distance from the axis of rotation B) Mass and velocity C) Force and velocity D) Mass and acceleration

3. If a force of 10 N is applied at a perpendicular distance of 0.5 m from the pivot of a lever, what is the torque produced?

A) 2 N·m B) 5 N·m C) 10 N·m D) 20 N·m

4. Angular momentum of a particle is given by:

A) r x p (where r is position vector and p is linear momentum) B) r x v (where r is position vector and v is velocity) C) m x v (where m is mass and v is velocity) D) I x ω (where I is moment of inertia and ω is angular velocity)

5. What is the SI unit of angular momentum?

A) Joule-second (J·s) B) Newton-meter (N·m) C) Kilogram-meter²/second (kg·m²/s) D) Radian/second (rad/s)

6. The law of conservation of angular momentum states that if the net external torque acting on a system is zero, then:

A) The total angular momentum of the system remains constant B) The total linear momentum of the system remains constant C) The total kinetic energy of the system remains constant D) The total potential energy of the system remains constant

7. An ice skater spins faster when she pulls her arms closer to her body. This is an example of:

A) Conservation of angular momentum B) Conservation of linear momentum C) Conservation of energy D) Newton's first law of motion

8. If a rigid body is rotating about a fixed axis, the torque is related to its angular acceleration by:

A) τ = Iα (where I is moment of inertia and α is angular acceleration) B) τ = L/t (where L is angular momentum and t is time) C) τ = Fd (where F is force and d is distance) D) τ = mvr (where m is mass, v is velocity, and r is radius)

9. A particle of mass m moves with a constant velocity v. Its angular momentum about the origin is:

A) Constant if the velocity vector passes through the origin B) Always zero C) Constant regardless of the origin's position D) Zero only if the particle is at rest

10. Which of the following is a vector quantity?

A) Torque B) Moment of inertia C) Mass D) Angular velocity magnitude

11. The moment of inertia of a point mass m at a distance r from the axis of rotation is given by:

A) mr² B) mvr C) mr D) mv²/r

12. For a system of particles, the total angular momentum is the:

A) Vector sum of the angular momenta of individual particles B) Scalar sum of the angular momenta of individual particles C) Average of the angular momenta of individual particles D) Product of the angular momenta of individual particles

13. A planet revolves around the Sun. If the gravitational force between them is considered, is angular momentum conserved?

A) Yes, because the gravitational force is a central force and produces no torque about the Sun B) No, because the planet is in motion C) Yes, because the planet has mass D) No, because the Sun has mass

14. When a diver tucks their body during a somersault, their angular velocity increases. This is due to:

A) Decrease in their moment of inertia B) Increase in their moment of inertia C) Constant moment of inertia D) External torque

15. What is the direction of the torque vector for a force applied tangentially to a circle of radius r?

A) Perpendicular to the plane of rotation B) Along the radius C) Along the tangent D) Opposite to the force

16. If the angular momentum of a system is L and it changes to L' in time Δt, the average external torque is given by:

A) (L' - L) / Δt B) L' * Δt C) L / Δt D) (L + L') / Δt

17. The moment of inertia of a rigid body depends on:

A) Mass distribution and the axis of rotation B) Total mass only C) Angular velocity only D) Applied torque only

18. A force F acts at point P. The torque about a point O is given by:

A) r x F (where r is the vector from O to P) B) F x r (where r is the vector from O to P) C) r * F (where r is the distance from O to P) D) F / r (where r is the distance from O to P)

19. If a body is rotating with constant angular velocity, what is the net external torque acting on it?

A) Zero B) Non-zero but constant C) Variable D) Equal to its angular momentum

20. A particle is moving in a straight line with constant speed. Its angular momentum about any point on the line of motion is:

A) Zero B) Constant and non-zero C) Increasing D) Decreasing

21. Which quantity is the rotational analogue of mass?

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

22. Which quantity is the rotational analogue of force?

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

23. Which quantity is the rotational analogue of linear momentum?

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

24. A particle of mass 2 kg is moving with a velocity of 3 m/s along the x-axis at y = 4 m. What is its angular momentum about the origin?

A) 24 kg·m²/s (in the +z direction) B) 18 kg·m²/s (in the +z direction) C) 12 kg·m²/s (in the -z direction) D) Zero

25. The torque required to change the angular momentum of a system from L1 to L2 in time t is:

A) (L2 - L1) / t B) (L1 - L2) / t C) L1 * t / L2 D) L2 * t / L1

26. A uniform rod of mass M and length L is rotating about its center. If a force is applied at one end perpendicular to the rod, it produces:

A) Angular acceleration B) Linear acceleration C) Constant angular velocity D) Constant angular momentum

27. When a spinning top is on the verge of falling, its axis of rotation starts to wobble. This phenomenon is known as:

A) Precession B) Nutation C) Gyroscopic effect D) Resonance

28. The rate of change of angular momentum of a particle is equal to:

A) The net external torque acting on it B) The net external force acting on it C) The moment of inertia D) The angular velocity

29. A force of 5 N is applied at a distance of 20 cm from the pivot. What is the torque if the force is applied at an angle of 30 degrees to the lever arm?

A) 0.5 N·m B) 1 N·m C) 0.866 N·m D) 2 N·m

30. If a body has zero net torque, its angular momentum:

A) Remains constant B) Becomes zero C) Increases linearly with time D) Decreases linearly with time

31. The moment of inertia of a thin ring of mass M and radius R about an axis through its center and perpendicular to its plane is:

A) MR² B) ½MR² C) ²⁄₃MR² D) ML²

32. A satellite in an elliptical orbit around the Earth has its angular momentum conserved because:

A) The gravitational force is a central force B) The satellite's speed is constant C) The distance from the Earth is constant D) There is no atmosphere in space

33. When a dancer pulls their legs and arms inwards, their angular speed increases. This is a direct consequence of:

A) Conservation of angular momentum B) Conservation of linear momentum C) Conservation of kinetic energy D) Change in mass

34. Torque is a vector quantity. Its direction is determined by:

A) The right-hand rule B) The left-hand rule C) The direction of the force D) The direction of the lever arm

35. What is the angular momentum of a particle of mass m moving with velocity v at a position r from the origin if r and v are perpendicular?

A) mvr B) mv/r C) mr/v D) Zero

36. A system is in equilibrium if:

A) Net force and net torque are both zero B) Net force is zero and net torque is non-zero C) Net force is non-zero and net torque is zero D) Net force and net torque are both non-zero

37. The moment of inertia of a solid sphere of mass M and radius R about an axis through its center is:

A) ²⁄₅MR² B) MR² C) ½MR² D) ML²

38. If the distance of the force from the axis of rotation is doubled, the torque:

A) Is doubled B) Is halved C) Remains the same D) Becomes zero

39. A particle is projected with velocity v. What is the torque of gravity about the point of projection?

A) Zero B) Non-zero and constant C) Increases with time D) Decreases with time

40. Which of the following statements is true about angular momentum?

A) It is conserved in the absence of external torque. B) It is always zero for a moving particle. C) Its direction is always along the velocity vector. D) It is a scalar quantity.

41. A flywheel is spinning at a constant rate. This implies:

A) The net torque on the flywheel is zero B) The moment of inertia is zero C) The angular momentum is zero D) The angular acceleration is non-zero

42. The angular momentum of a particle of mass m with position vector r and velocity v is given by:

A) m(r × v) B) m(v × r) C) m(r · v) D) m(r + v)

43. A force is applied at the center of a wheel. The torque produced about the center is:

A) Zero B) Maximum C) Dependent on angular velocity D) Dependent on moment of inertia

44. What is the condition for rotational equilibrium?

A) Sum of clockwise torques = Sum of anticlockwise torques B) Sum of clockwise torques > Sum of anticlockwise torques C) Sum of clockwise torques < Sum of anticlockwise torques D) Torque is maximum

45. The moment of inertia of a hollow sphere of mass M and radius R about an axis through its center is:

A) ²⁄₃MR² B) MR² C) ½MR² D) ML²

46. If a force vector and the position vector are collinear, the torque produced is:

A) Zero B) Maximum C) Infinite D) Equal to the force

47. Which of the following is a unit of torque?

A) Newton-meter B) Joule C) Watt D) Pascal

48. A particle moves in a circle of radius r with constant speed v. Its angular momentum about the center of the circle is:

A) mvr B) mv/r C) mr/v D) Zero

49. The change in angular momentum of a body is directly proportional to the applied:

A) Torque and the time interval B) Force and the time interval C) Moment of inertia and angular velocity D) Angular acceleration and angular velocity

50. A boy is standing on a rotating platform holding weights. If he extends his arms outwards, his angular velocity will:

A) Decrease B) Increase C) Remain the same D) Become zero

Moment of a force, torque, angular momentum, conservation of angular momentum and applications - Online Test

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