Let the mass of the disc = M
Therefore, the mass of the removed part of disc, m = (M/R^2)*(R/2)^2 = M/4
Now the center of gravity of the resulting flat body,
R= [M*0 – (M/4)*(R/2)]/(M-M/4)
= -(MR/8)/(3M/4)
= -R/6
Negative sign shows that the center of gravity lies at opposite direction of the original COM at a distance R/6.