Figure shows a uniform disc of radius `R`, from which a hole of radius `R/2` has been cut out from left of the centre and is placed on the right of the centre of the disc. Find the CM of the resulting disc.

Explanation

Mass of the cut out disc is
`m=M/(piR^(2))xxpi(R/2)^(2)=M/4`
Let centre of the disc is at origin of the coordinates. Then we can write the CM of the system as
`x_(CM)=(vec(MR)-vec(mr)+vec(mr))/(M+m+m)=(Mxx0-M/4((-R)/2)+M/4(R/2))/(M-M/4+M/4)=R/4`
`y_(CM)=0`