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  4. 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. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-gvnmvhbsl9heotpq.jpg /> When string is cut, the initial angular acceleration of the rod is

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

NTA AbhyasNTA Abhyas 2022

Solution:

Torque on the rod = Moment of weight of the rod about $P$ .
Solution
$\tau=Mg\frac{L}{2}$ ..... (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 $
$\Rightarrow \alpha =\frac{3 g}{2 L}$