A $\operatorname{rod} P Q$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizont

Question

A $\operatorname{rod} P Q$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in figure.\ initial angular acceleration of the rod is\

Professor PC Thomas Classes · Answer

(c) :\ When the string is cut, the rod will rotate about $P$. Let $\alpha$ be initial angular acceleration of the rod. Then\ Torque, $	au=I \alpha=\frac{M L^{2}}{3} \alpha$\ Also, $	au=M g \frac{L}{2}$\ Equating (i) and (ii), we get $$ M g \frac{L}{2}=\frac{M L^{2}}{3} \alpha \quad 	ext { or } \quad \alpha=\frac{3 g}{2 L} $$