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. `(Iomega)/(I+mR^(2))`
B. `(Iomega+mvR)/(I+mR^(2))`
C. `(Iomega-mvR)/(I+mR^(2))`
D. `(Iomega-mvR)/(I)`

Answer

C

Explanation

`L_(1)=L_(2)`
implies `Iomega-mvR=(I+mR^(2))omega`
implies `omega=(Iomega-mvR)/((I+mR^(2)))`