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A uniform rod...

Question

A uniform rod AB of mass $m$ and length $2 a$ is falling freely without rotation under gravity with AB horizontal. Suddenly the end A is fixed when the speed of the rod is $v$ . The angular speed with which the rod begins to rotate is

A

\frac{v}{2 a}

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B

\frac{4 v}{3 a}

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C

\frac{v}{3 a}

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D

\frac{3 v}{4 a}

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Solution

The correct option is D $\frac{3 v}{4 a}$
Angular momentum about point O is conserved.
Let the angular velocity be w.
$L_{i} = L_{f}$
$m v a = I_{O} w$
$m v a = \frac{1}{3} m (2 a)^{2} w$
$⟹ w = \frac{3 v}{4 a}$

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