Question

A uniform thin rod of mass $m$ and length $l$ is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes and angle $\theta$ with horizontal.

Answer 1

Since COM moves in a straight line work done by gravity

$mg\frac{l}{2}-mg\frac{l}{2}sin\theta =\frac{1}{2}m{v}^{2}g\frac{l}{2}(1-sin\theta )=\frac{1}{2}{v}^{2}v=\sqrt{gl(1-sin\theta )}$