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Question

A cockroach of mass m is moving on the rim of a disc with velocity V in the anticlockwise direction. The moment of inertia of the disc about its own axis is I and it is rotating in the clockwise direction with angular speed ω. If the cockroach stops moving then the angular speed of the disc will be

A
IωI+mR2
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B
Iω+mVRI+mR2
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C
IωmVRI+mR2
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D
IωmVRI
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Solution

The correct option is C IωmVRI+mR2
Angular momentum of the cockroach about the axis passing through the center of the disc: Lc=mVR
Angular momentum of the disc Ld=Iω
Ltotal=Lc+Ld=IωmVR since both angular momentum are opposite to each other.
When the cockroach stops moving, due to conservation of angular momentum,
(I+mR2)ω=IωmVR
ω=IωmVRI+mR2

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