A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the cirucmferences of the discs coincide. The centre of mass of the new disc is `alpha/R` from the center of the bigger disc. The value of `alpha` is

Explanation

mass of cut off portion `m=(pi(R)^(2)M)/(pi(2R)^(2))=M/4` and position of its centre of mass, `OO_(1)=R`
hence, for remaining part (new disc)
`x_(CM)=alphaR=(Mxx0-(M/4)xxR)/(M-M/4)=-R/3 rArralpha=-1/3`