Question

A solid sphere and a hollow sphere have same mass and radius. Ratio of radius of gyration of the solid sphere to that of the hollow sphere about a tangent axis is:

• A. $\sqrt{\frac{7}{3}}$
• B. $\sqrt{\frac{3}{5}}$
• C. $\sqrt{\frac{5}{3}}$
• D. $\sqrt{\frac{21}{5}}$

Answer 1

The correct option is B $\sqrt{\frac{3}{5}}$

For hollow sphere, movement of inertia $=\frac{2}{3}M{R}^2$
$M{K}^2=\frac{2}{3}M{K}^2$
or $K=\sqrt{\frac{2}{3}R}$
For solid sphere, movement of inertia $=\frac{2}{5}M{R}^2$
$M{K_1}^2=\frac{2}{5}M{K}^2$
or $K_1=\sqrt{\frac{2}{5}R}$
Now, $\frac{K_1}{K}=\sqrt{\frac{3}{5}}$