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Question

A homogeneous rod AB of length L and mass M is pivoted at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in the horizontal position. An insect S of the same mass M falls vertically with speed V on the point C mid-way between O and B. The initial angular velocity ω in terms of V and L is


A

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B

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C

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D

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Solution

The correct option is B



Consider the rod and insect as a single system.
We can conserve the angular momentum of the system w.r.t centre 'O' of the rod.

Li = Initial angular momentum = MV(L4)
Lf = Final angular momentum = (ML212)ω+M(L4)2ω
MV(L4)=ω(ML212+ML216)
ω=12V7L


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