Question

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.

Answer 1

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`