Find the position of centre of mass of a uniform disc of radius R from which a hole of radius r is cut out. The centre of the hole is at a distance R2 from the centre of the disc.

For a disc, mass is proportional to surface area. SoMass of cut portion: m1 = kπr2,Mass of remaining portion: m2 = kπ(R2-r2)Apply m1x1 = m2x2 where x1 = R2, and solve to getx2 = Rr22(R2-r2)