Let \(\vec{F}\) be a force acting on a particle having position vector \(\vec{r}\). Let \(\vec{\tau}\) be the torque of this force about the origin, then:

A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude

1. zero

2. Mga

3. Mga sin θ

4. \(\frac{1}{2}\) Mga sin θ

Consider the following two equations
            (A) L = I ω    (B) \(\frac{dL}{dt}=\Gamma\)
In noninertial frames:

1. both A and B are true

2. A is true but B is false

3. B is true but A is false

4. both A and B are false

The density of a rod gradually decreases from one end to the other. It is pivoted at an end so that it can move about a vertical axis through the pivot. A horizontal force F is applied on the free end in a direction perpendicular to the rod. The quantities, that do not depend on which end of the rod is pivoted, are

1. angular acceleration

2. angular velocity when the rod completes one rotation

3. angular momentum when the rod completes one rotation

4. torque of the applied force