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

Answer 1

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

When string is cut, rod will rotate about 'P'
$\therefore Torque,\tau =\frac{Mg\times L}{2}$ ...(1)

if $\alpha$ is initial acceleration, then,
$\tau =I\alpha =\frac{M{L}^2}{3}\alpha$ ...(2)
where I = moment of inertia of rod about one end = $\frac{M{L}^2}{3}$,
equating (1) and (2)
$\frac{Mg\times L}{2}=\frac{M{L}^2}{3}\alpha$
$\alpha =\frac{3g}{2L}$