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

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

Answer 1

The correct option is D $\frac{3g}{2L}$


Weight of the rod will produce the torque

Hence torque on rod $=$ Moment of weight of rod about $P$

We also know that $(\tau =I\alpha )$,

$\tau =mg\frac{L}{2}=I\alpha =\frac{m{L}^2}{3}\alpha [\because I_{rod}\text{about point}P=\frac{M{L}^2}{3}]$
Hence, angular acceleration $\alpha =\frac{3g}{2L}$
Therefore the correct option is D