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

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Solution

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Li=MVL/2

Lf=Iω

Since both rods stick together it becomes a rod of mass 2M and length 2L

Hence, Lf=Iω=(2M)(2L)212ω

Equating Li=Lf

⇒MVL/2=23ML2ω

⇒ω=34VL

The rod which has the velocity is sticking to the stationary rod which is at the top. After sticking the inertia of the stationary rod will make the whole rod to rotate in counterclockwise direction. Hence A and C is correct.

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