Question

A uniform rod of length $1m$ and mass $2kgs$ is suspended. Calculate tension $T$ (in N) in the string at the instant when the right string snaps $(g=10m/s^2)$

Answer 1

The rod will rotate about the end in contact with the rope .

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:

$mg-T=ma$

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