Question

Find the M.I. of a uniform semicircular disc of mass M and radius 'R' about an axis perpendicular to its plane and passing through point 'P' as shown.

Answer 1

given$L^2=3R^2$

M.O.I of solid cylinder about its own axis = $\frac{1}{2}M{R}^2$

M.O.I about an axis perpendicular to center of gravity = $M(\frac{L^2}{12}+\frac{R^2}{4})$