Question

The angular velocity of a body changes from ${\omega }_1$ and ${\omega }_2$ without applying a torque but the moment of inertia changes. The ratio of corresponding radii of gyration 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

Answer: (C)

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

Angular momentum will be equal in both cases also,
$m{k}_1^2$ and $m{k}_2^2$ are corresponding Moment of Inertia

of two different cases in question

Hence,
$m{k}_1^2{\omega }_1=m{k}_2^2{\omega }_2$
$\frac{K_1}{K_2}=\sqrt{\frac{{\omega }_2}{{\omega }_1}}$