Question

A straight rod AB of mass M and length L is placed on a frictionless horizontal surface. a horizontal force having constant magnitude F and a fixed direction starts acting at the end A. The rod is initially perpendicular to the force. Find the initial acceleration of end B.

Answer 1

Initially the rod is perpendicular to the force . So the moment of force about end B is $=F.AB=F.L$

The moment of inertia of the rod about a axis passing through and B and perpendicular to its length is.

$I=\frac{1}{3}M{L}^2$

If initil acceleration of rod $\alpha$

Torque applied on the rod about B = Moment of force about B

$⟹I\alpha =F.L$

$⟹\frac{1}{3}M{L}^2\alpha =F.L$

$⟹\alpha =\frac{3F}{ML}$