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

Options

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)`

Answer

C

Explanation

`L_(1)= L_(2)`
`rArr I omega- mv R= (I + mR^(2)) omega`
`rArr omega= (I omega - mvR)/((I + mR^(2)))`