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

• Correct answer
  A

  $\frac{3 g}{2 L}$
• B

  $\frac{G}{L}$
• C

  $\frac{2 g}{L}$
• D

  $\frac{2 g}{3 L}$

Solution

Torque on the rad = Mament of weight of the rod about $\rho$ $\tau=m g \frac{1}{2}$ $\because$ Moment of inertia of rod about $P=\frac{M L^2}{3}$ As $\tau=1 \alpha$ From Eqs. (i) and (ii), we get $\begin{aligned} & M g \frac{L}{2}=\frac{M L^2}{3} \alpha \\ \therefore \alpha & =\frac{3 g}{2 L} \end{aligned}$

Hence, the correct answer is option: 'A'.