$A$ body changes its angular speed from $\omega_1$ to $\omega_2$ without any external torque applied. This change is due to a change in its moment of inertia. What is the ratio of the radii of gyration in the two cases?

• A
  $\sqrt{\omega_2} : \sqrt{\omega_1}$
• B
  $\sqrt{\omega_1} : \sqrt{\omega_2}$
• C
  $\omega_1 : \omega_2$
• D
  $\omega_2 : \omega_1$