$A$ thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$. 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:

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