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A bar of mass $M$ and length $L$ is in pure translatory motion with its center of mass velocity $v$ . it collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length $2 L$ ). The angular velocity of the composite bar will be:

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$\frac{3 v}{4 L}$ clockwise

$\frac{4 v}{3 L}$ clockwise

$\frac{3 v}{4 L}$ counter clockwise

$\frac{v}{L}$ counter clockwise

answer is C.

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Detailed Solution

By conservation of angular momentum about $C . M,$ we have

$M v \frac{L}{2} = I ω = \frac{2 M {(2 L)}^{2}}{12} ω$

$ω = \frac{3 v}{4 L}$ counter clockwise

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