Question

The density of a rod continuously increases from A to B. It is easier to set it into rotation by :

• A. clamping the rod at A and applying a force F at B, perpendicular to the rod
• B. clamping the rod at B and applying a force F at A, perpendicular to the rod
• C. clamping the rod at mid point of AB and applying a force F at A, perpendicular to the rod
• D. clamping the rod at mid-point of AB and applying force F to B, perpendicular to the rod.

Answer 1

The correct option is B clamping the rod at B and applying a force F at A, perpendicular to the rod

$\tau =I\alpha$

For the rod to rotate easily, the torque should be maximum and $I$ should be minimum.

For torque to be maximum, the force must be applied to the farthest distance to the clamping point.

$I$ is minimum when the center of mass is closer to the clamping point (rotational axis).

Thus it is easier to set it into rotation by clamping the rod at B and applying a force F at A, perpendicular to the rod.