A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance aR from the centre of the bigger disc. The value of a is

Explanation

mass of cutoff portion `m = (pi(r )^(2)M)/([i(2R)^(2) = M/4])` and
position of its centre of mass , `OO_(1) = R` hence , for remaining part (new disc)
`x_(CM) = alpha R = (Mxx 0 - (M/4)xxR)/(M-M/4 ) = - R/3 rArr alpha = - 1/3`