Physics - Rotation Question with Solution | TestHub

The moment of inertia of a solid sphere about its diametric axis is given by:

$I=\frac{2}{5}m{R}^2$

According to the theorem of parallel axes, the moment of inertia of the sphere about a tangent is:

$I_T=I_{cm}+m{R}^2$

$I_T=\frac{2}{5}m{R}^2+m{R}^2=\frac{7}{5}m{R}^2$

Expressing $I_T$ in terms of $I$:

$I_T=\frac{7}{2}\left(\frac{2}{5}m{R}^2\right)=3.5I$

Answer: $3.5\mathrm{I}$