Question

The angular speed of a body changes from $\omega_1$ to $\omega_2$ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is

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

Answer 1

Answer: (B)

$\sqrt{\omega_2}:\sqrt{\omega_1}$

Answer 2

In the absence of external torque $I_1 \omega_1=I_2 \,\omega_2$ or $MK^2_1\,\omega_1=MK^2_2\, \omega_2$ $=\frac{K_1}{K_2}=\sqrt{\frac{\omega_2}{\omega_1}}$