A thin circular ring of mass `m` and radius `R` is rotating about its axis with a constant angular velocity `omega`. Two objects each of mass `M` are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity `omega' =`

Options

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

Answer

D

Explanation

Applying conservation of angular momentum `I.omega.=Iomega`
`(mR^(2)+2MR^(2))omega.=mR^(2)omegaimpliesomega.=omega[(m)/(m+2M)]`