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

As no external torque is acting about the axis, angular momentum of system remains conserved.

`therefore l_(1)omega=l_(2)omega' rArr mR^(2)omega=(mR^(2)+2MR^(2))omega'`
`rArr" "omega'=((m)/(m+2M))omega`