Question

The angular speed of a body changes from ${\omega }_1$ to ${\omega }_2$ without applying a torque but due to changes in moment of inertia. The ratio of radii of gyration in two cases is

• A. $\sqrt{{\omega }_2}:\sqrt{{\omega }_1}$
• B. 1
• C. $\sqrt{{\omega }_2^2}:\sqrt{{\omega }_1^2}$
• D. $\sqrt{{\omega }_2^3}:\sqrt{{\omega }_1^3}$

Answer 1

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

$I_1{\omega }_1=I_2{\omega }_2$
$M{K}_1^2{\omega }_1=M{K}_2^2{\omega }_2$
${\left(\frac{K_1}{K_2}\right)}^2=\frac{{\omega }_2}{{\omega }_1}\Rightarrow \frac{K_1}{K_2}=\sqrt{{\omega }_2}:\sqrt{{\omega }_1}$