Q18 of 149 Page 192

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?

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.


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