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

Answer

A

Explanation

According to conservation of momentum,
`L=L.`
`therefore I_(1)omega=I.omega.`
`MR^(2)omega=(MR^(2)+2mR^(2))omega.(because I.=MR^(2)+(2m)R^(2))`
`therefore Momega=(M+2m)omega.`
`therefore omega.=(M)/(M+2m).omega`