Question

Find the ratio of radius of gyration of a solid sphere about its diameter to radius of gyration of hollow sphere about its tangent.(Given Radius of both the spheres is same)

Answer 1

Radius of a gyation of a solid sphere about its diameter $(I_k{)}_1=\sqrt{\frac{2}{5}}R$
Radius of gyation of a Hellow about its tangent $\Rightarrow (I_k{)}_2=\sqrt{\frac{5}{3}}R$
$\therefore \frac{I_k{)}_1}{(I_k{)}_2}=\frac{\sqrt{\frac{2}{5}}R}{\sqrt{5}3R}$