$A$ hemispherical shell of mass $2M$ and radius $6R$ and a point mass $M$ are performing circular motion due to their mutual gravitational interaction. Their positions are shown in the figure at any moment of time during motion. If $r_1$ and $r_2$ are the radii of the circular paths of the hemispherical shell and the point mass respectively,and $\omega_1$ and $\omega_2$ are the angular speeds of the hemispherical shell and the point mass respectively,then choose the correct option.

• A
  $\omega_1 = \sqrt{\frac{GM}{18R^3}}$
• B
  $\omega_2 = \sqrt{\frac{GM}{24R^3}}$
• C
  $\omega_1 = \sqrt{\frac{GM}{36R^3}}$
• D
  $\omega_2 = \sqrt{\frac{GM}{72R^3}}$