Question

A solid cylinder has mass M, radius R and length l. Its moment of inertia about an axis passing through its center and perpendicular to its own axis is

Answer 1

Let, XX' be the axis of symmetry and YY' be the axis perpendicular to XX'. 

Let us consider a circular disc S of width dx at a distance x from YY' axis. 

Mass per unit length of the cylinder is M/I​. 

Thus, the mass of disc is M/Idx

Moment of inertia of this disc about the diameter of the rod = \((\frac{M}{I}dx) \frac{R^2}{4}.\)

Moment of inertia of disc about YY' axis given by parallel axes theorem is = \((\frac{M}{I}dx) \frac{R^2}{4}\) + \((\frac{M}{I}dx) x^2\)

Moment of inertia of cylinder,