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)`
C. `(omegam)/((m+M))`
D. `(omegam)/((2m+M))`

Answer

D

Explanation

As no external torque is acting on the system, therefore, angular momentum of the system is conserved.
`I_(1)omega=I_(2)omega.`
`mR^(2)omega=(mR^(2)+2MR^(2))omega.`
`omega.=((m)/(m+2M))omega`