First slide

Torque

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

Moderate

A

$\frac{2 g}{L}$
B

$\frac{2 g}{2 L}$
C

$\frac{3 g}{2 L}$
D

$\frac{g}{L}$

Solution

When the string is cut, the rod will rotate about P. Let $α$ be initial angular acceleration of the rod. Then
$T o r q u e, τ = I α = \frac{M L^{2}}{3} α - - - (i) (∵ M o m e n t o f i n e r t i a o f t h e r o d a b o u t o n e e n d = \frac{M L^{2}}{3}) A l s o, τ = M g \frac{L}{2} - - - (i i) E q u a t i n g (i) a n d (i i), w e g e t M g \frac{L}{2} = \frac{M L^{2}}{3} α o r α = \frac{3 g}{2 L}$

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