Question

Find the moment of inertia of a solid cylinder of mass $M$ and radius $R$ about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Answer 1

The moment of inertia of the cylinder about its axis is $\frac{M{R}^2}{2}$
Using parallel axis theorem
$I=I_0+M{R}^2=\frac{M{R}^2}{2}+M{R}^2=\frac{3}{2}M{R}^2$
Similarly, the moment of inertia of a solid sphere about a tangent
$\frac{2}{5}M{R}^2+M{R}^2=\frac{7}{5}M{R}^2$