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A cockroach is moving with velocity v in...

A cockroach is moving with velocity `v` in anticlockwise direction on the rim of a disc of radius `R` of mass `m`. The moment of inertia of the disc about the axis is `I` and it is rotating in clockwise direction with an angular velocity `omega`. If the cockroach stops, the angular velocity of the disc will be

A

`(I omega)/(I + mR^(2))`

B

`(I omega + mvR)/(I + m R^(2))`

C

`(I omega - mvR)/(I+ mR^(2))`

D

`(I omega- mvR)/(I)`

Text Solution

Verified by Experts

The correct Answer is:
C
`L_(1)= L_(2)`
`rArr I omega- mv R= (I + mR^(2)) omega`
`rArr omega= (I omega - mvR)/((I + mR^(2)))`
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