Question

A uniform rod $AB$ of mass $2kg$ is hinged at one end $A$. The rod is kept in the horizontal position by a massless string tied at point $B$. Find the reaction of the hinge (in N) on end $A$ of the rod at the instant when string is cut. $(g=10m/s^2)$

Answer 1

The rod will rotate about the end A.

Let a be the linear acceleration of COM of rod and $\alpha$ be the angular acceleration.

$\alpha =\frac{\tau }{I}=\frac{mg\frac{l}{2}}{\frac{m{l}^2}{3}}=\frac{3g}{2l}$

$a=\frac{l}{2}\alpha =\frac{l}{2}\frac{3g}{2l}=\frac{3g}{4}$

From force equation:

$mg-F=ma$

$F=mg-m\frac{3g}{4}=m\frac{g}{4}=\frac{20}{4}=5$