$A$ thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2 \; rad \; s^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring,the ring will then rotate with an angular velocity (in $rad \; s^{-1}$) of:

• A
  $\frac{M}{M+m}$
• B
  $\frac{M+2m}{2M}$
• C
  $\frac{2M}{M+2m}$
• D
  $\frac{2(M+2m)}{M}$