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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.
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B
angular velocity when the rod completes one rotation.
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C
angular momentum when the rod completes one rotation.
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D
torque of the applied force.
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Solution

The correct option is B 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 α=ar is different. Also the angular velocity ω=vr is different. Also the angular momentum which depends on I and ω 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.

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