Physics - Rotation Question with Solution | TestHub

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about its diameter (an axis passing through its centre) is given by:

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

Using the parallel axis theorem, the moment of inertia $I$ about an axis parallel to the diameter and at a distance $d=\frac{R}{3}$ from the centre is:

$I=I_{cm}+M{d}^2$

Substituting the values:

$I=\frac{2}{5}M{R}^2+M{\left(\frac{R}{3}\right)}^2$

$I=\frac{2}{5}M{R}^2+\frac{1}{9}M{R}^2$

$I=\left(\frac{18+5}{45}\right)M{R}^2$

$I=\frac{23}{45}M{R}^2$