Question

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 though 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
(a) angular acceleration
(b) angular velocity when the rod completes one rotation
(c) angular momentum when the rod completes one rotation
(d) torque of the applied force.

Answer 1

The quantities, that do not depend on which end of the rod is pivoted, are torque of the applied force.

Explanation :                

• The center of mass would be different in both cases.
• Thus the distance between the axis of rotation r and the center of mass would be different for both cases, indicating the angular acceleration is different.  
• Also the angular velocity ω = $\frac{v}{r}$ is different.
• The angular momentum which depends on I and ω will also be different.
• The torque produced by the external force F and the only quantity between the force and the rotational axis that remains the same in both cases.

Therefore, option (d) is the correct answer.