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)`