The density of a rod AB continuously increases from A to B. Is it easier to set it in rotation by clamping it at A and applying a perpendicular force at B or by clamping it at B and applying the force at A?

Question

The density of a rod AB continuously increases from A to B. Is it easier to set it in rotation by clamping it at A and applying a perpendicular force at B or by clamping it at B and applying the force at A?

Philoid · Accepted Answer

When there is no constrains attached, the whole mass is concentrated at the center of mass of the rod which is more towards B as the mass concentration is higher.

From the diagram,

Now, moment of inertia,

So, the first one is easier to rotate.