Question

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

• A. $\sqrt{3}:\sqrt{5}$
• B. $\sqrt{12}:\sqrt{3}$
• C. $1:\sqrt{3}$
• D. $\sqrt{5}:\sqrt{6}$

Answer 1

Answer: (D)

For a disc moment of inertia about a tangential axis in its own plane $=\frac{5}{4}M{R}^2$
$\therefore M_1{K}_1^2=\frac{5}{4}{M}_1{R}^2$
$\Rightarrow K_1=\frac{\sqrt{5}}{2}R$
Now, for a ring moment of inertia about a tangential axis in its own plane $=\frac{3}{2}{M}_2{R}^2$
$\therefore M_2{K}_2^2=\frac{3}{2}{M}_2{R}^2$
$\Rightarrow K_2=\sqrt{\frac{3}{2}}R$
$\therefore \frac{K_1}{K_2}=\frac{\sqrt{5}}{\sqrt{6}}$