Question

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

• A. $\sqrt{3}:\sqrt{2}$
• B. $1:\sqrt{2}$
• C. $\sqrt{2}:1$
• D. $\sqrt{2}:\sqrt{3}$

Answer 1

The correct option is B $1:\sqrt{2}$

Say $K$ is radius of gyration
Moment of inertia, $I=M{K}^2$
For disc,
Moment of inertia, $I_d=\frac{M{R}^2}{2}=M{K}_d^2⟹K_d=\frac{R}{\sqrt{2}}$
Similarly for ring,
Moment of inertia, $I_r=M{R}^2=M{K}_r^2⟹K_r=R$

$\therefore K_d:K_r=1:\sqrt{2}$