Question

A square plate $ABCD$ of mass $m$ and side $l$ is suspended with the help of two ideal strings $P$ and $Q$ as shown. determine the acceleration $\left(inm/s^2\right)$ of corner $A$ of the square just at the moment the string Q is cut $(g=10m/s^2)$

Answer 1

Let the centre of mass of the block move down with an acceleration $a$.

$mg-T=ma$

Let the block have an angular acceleration $\alpha$ about its centre of mass.

The point A has only horizontal acceleration at the instant at which the string Q is cut.

$T\frac{l}{2}=\frac{m{l}^2}{6}\alpha \alpha \frac{l}{\sqrt{2}}\cos 45=a$

$a=6m{s}^{-2}$