The angular velocity of a body changes from ${\mathrm{\omega }}_1\text{ to }{\mathrm{\omega }}_2$ without applying torque but changing moment of inertia. The ratio of initial radius of gyration to the final radius of gyration is 

• A

  ${\mathrm{\omega }}_2:{\mathrm{\omega }}_1$

• B

  ${\mathrm{\omega }}_2^2:{\mathrm{\omega }}_1^2$

• C

  $\sqrt{{\mathrm{\omega }}_2}:\sqrt{{\mathrm{\omega }}_1}$

• D

  $1/{\mathrm{\omega }}_2:1/{\mathrm{\omega }}_1$