Question

The angular velocity of a body changes from ${\omega }_1$ to ${\omega }_2$ without applying a torque but by changing the moment of inertia. The ratio of corresponding radii of gyration $K_1:K_2$ is:

• A. ${\omega }_1:{\omega }_2$
• B. $\sqrt{{\omega }_1}:\sqrt{{\omega }_2}$
• C. $\sqrt{{\omega }_2}:\sqrt{{\omega }_1}$
• D. ${\omega }_2:{\omega }_1$

Answer 1

The correct option is C $\sqrt{{\omega }_2}:\sqrt{{\omega }_1}$

Since the net torque applied is zero, therefore angular momentum will be conserved.

So, $m{K}_1^2{\omega }_1=m{K}_2^2{\omega }_2$

So, $\frac{K_1}{K_2}=\sqrt{\frac{{\omega }_2}{{\omega }_1}}$