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JEE MainPhysicsModerateRigid Body Dynamics

A bar of mass M & length L is in pure translatory motion with
its centre 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

Show answer and solution
Cons. of ang. momentum about P gives
MVL2=(2M)(2L)212wMV\frac{L}{2} = \frac{(2M)(2L)^{2}}{12}w
⇒V2=2Lw3\Rightarrow \frac{V}{2} = \frac{2Lw}{3}
w=3V4Lw = \frac{3V}{4L}

Source: Grass-G / P-07 Physics paper 17 October.docx

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