Physics - Rotation Question with Solution | TestHub

Moment of inertia of a circular disc about its central axis is $I_{disc}=\frac{1}{2}M{R}^2$.

Radius of gyration of the disc is $K_{disc}=\sqrt{\frac{I_{disc}}{M}}=\frac{R}{\sqrt{2}}$.

Moment of inertia of a circular ring about its central axis is $I_{ring}=M{R}^2$.

Radius of gyration of the ring is $K_{ring}=\sqrt{\frac{I_{ring}}{M}}=R$.

Ratio of their radii of gyration is $\frac{K_{disc}}{K_{ring}}=\frac{\frac{R}{\sqrt{2}}}{R}=\frac{1}{\sqrt{2}}$.

The ratio is $1:\sqrt{2}$.

Answer: $1:\sqrt{2}$