From a disc of mass `m` and radius `r`, a circular portion of radius `(r )/(3)` is removed from the edges. Find the M.O.I of the remaining system about a normal through center of original disc

Explanation

Let `I_(2)` be the M.I. of remaining poriton.
M.I of the removed partion about a normal axis through centre of the original disc is
`I_(1)=((m)/(9)((r )/(3))^(2))/(2)+(m)/(9)((2r)/(3))^(2)` or `I_(1)=(mr^(2))/(18)`
Hence, M.I. of the remaining portion is
`I_(2)=I-I_(1)=(mr^(2))/(2)-(mr^(2))/(18)` or `I_(2)-(4mr^(2))/(9)`