Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

As the torque applied on the given body is zero, we can conserve its angular momentum.
i.e., $L_1-L_2$
$\Rightarrow I_1{\omega }_1=I_2{\omega }_2$
$\left(M{K}_1^2\right){\omega }_1=\left(M{K}_2^2\right){\omega }_2$
$\Rightarrow \frac{K_1}{K_2}=\sqrt{\frac{{\omega }_2}{{\omega }_1}}=\sqrt{{\omega }_2}:\sqrt{{\omega }_1}$