A uniform thin circular ring of mass M and radius R is rotating about its fixed axis passing through its centre, perpendicular to its plane of rotation with constant angular velocity w. Two objects each of mass m are gently attached to the opposite ends of the diameter of the ring. The ring now rotates with an angular velocity

Question

$$\begin {array} {1 1} (a)\;\frac{wM}{(M+m)} & \quad (b)\;\frac{wM}{M+2m)} \\ (c)\;\frac{COM}{(M-2m)} & \quad  (d)\;\frac{w (M+2m)}{M} \end {array}$$