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 through the pivot. A horizontal force $F$ is applied on the free end in a direction perpendiclar 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

Answer: (D)

torque of the applied force.

The center of mass in both the cases would be different. Thus the distance between the center of mass and the rotational axis r would be different for both the cases implying that the angular acceleration $\alpha =\frac{a}{r}$ is different. Also the angular velocity $\omega =\frac{v}{r}$ is different. Also the angular momentum which depends on $I$ and $\omega$ will also be different. The torque by the external force which is the product of $F$ and the distance between force and the rotational axis is the only quantity which will remain same for both the cases.