Physics - Rotation Question with Solution | TestHub

The moment of inertia of a solid sphere about an axis passing through its centre is $I_{cm}=\frac{2}{5}M{R}^2$.

Using the parallel axis theorem, the moment of inertia about a parallel axis at a distance $d$ from the centre is given by $I=I_{cm}+M{d}^2$.

Given $d=\frac{R}{3}$, substituting the values:

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

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

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

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

Answer: $23{\text{MR}}^2/45$