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Question

A homogeneous rod AB of length L and mass M is pivoted at the center 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 and sticks to it. The initial angular velocity ω in terms of V and L is :

A
6V7L
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B
12V7L
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C
24V7L
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D
V7L
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Solution

The correct option is B 12V7L
Since there is no external torque angular momentum will be conserved.

Li=MVL4 where M is the mass of the insect, V is the velocity of the insect and L4 is the distance of the point from center of the rod where the insect falls.
Lf=Iω=(ML212+M(L4)2)ω=7ML248ω
MVL4=7ML248ω
ω=12V7L


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