Question

A rod $PQ$ 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 the figure.

When string is cut, the initial angular acceleration of the rod is

• A. $\frac{3 g}{2 L}$
• B. $\frac{g}{L}$
• C. $\frac{2 g}{L}$
• D. $\frac{2 g}{2 L}$

Answer 1

Answer: (A)

Torque on the rod = Moment of weight of the rod about $P$ .

$\tau=Mg\frac{L}{2}$ ..... (i)
Moment of inertia of the rod about P
$I=\frac{M L^{3}}{3}$ ..... (ii)
As, $\tau=I\alpha$
From Eqs. (i) and (ii), we get
$Mg\frac{L}{2}=\frac{M L^{2}}{3}\alpha$
$\Rightarrow \alpha =\frac{3 g}{2 L}$