$A$ 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 will now 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
  $\frac{\omega (M + 2m)}{M}$