Question

Find the radius of gyration of a solid uniform sphere of radius R about its tangent.

Answer 1

Given,

A solid sphere having radius $R$

For solid sphere

$I_{cm}=\frac{2}{5}M{R}^2$

$I_{tangent}=I_{c}m+M{R}^2$

$=\frac{2}{5}M{R}^2+M{R}^2$

$=\frac{7}{5}M{R}^2$

Thus, the radius of gyration is $\sqrt{\frac{7}{5}}R$ Where M is constant