A thin circular ring of mass `M` and radius `R` is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity `omega`. If two objects each of mass `m` be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

Options

A. `(omegaM)/(M+m)`
B. `(omega(M-2m))/(M+2m)`
C. `(omegaM)/(M+2m)`
D. `(omega(M+2m))/(M)`

Answer

C

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)` by COAM
`omega_(2)=(I_(1)omega_(1))/(I_(2))`
`I_(1)=MR^(2)`
`omega_(1)=omega`
`I_(2)=MR^(2)+mR^(2)+mR^(2)=(M+2m)R^(2)`
`omega_(2)=(Momega)/(M+2m)`.