How to calculate the shift in com???

Question

A small disc of radius 2cm is cut from a disc of radius 6cm. If the distance between their centres is 3.2cm , what is the shift in the centre of mass of the disc?

Answer 1

Let the mass per unit area = m

M = mass of disc = πR2m = π(6)2m = 36πm

M1 = mass of removed disc = π(2)2m = 4πm

M2 = mass of remaining portion = M – M1 = 36πm – 4πm = 32πm

CM of disc is at origin

CM of removed disc = r1 = 3.2 cm.... (given)

CM of remaining disc = r2xad

hence