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

Question

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

TestHub · Accepted Answer

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

$τ = M g \frac{L}{2}$ ..... (i)

Moment of inertia of the rod about P

$I = \frac{M L^{3}}{3}$ ..... (ii)

As, $τ = I α$

From Eqs. (i) and (ii), we get

$M g \frac{L}{2} = \frac{M L^{2}}{3} α$

$\Rightarrow α = \frac{3 g}{2 L}$

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