Hello!!!

Hope you are doing great!!!

The radius of the bigger sphere=r

let x be the distance between center of mass from the original center of the sphere after the smaller sphere has cut.

let the density of the bigger sphere be d

mass of the bigger sphere = 4/3* π r^3d

mass of the smaller sphere= 4/3* π(r/2)^3d

mass of the remaining sphere= 4/3* π r^3d - 4/3* π(r/2)^3d

on solving,we get,,,, 7/6* π r^3d

position of the center of mass of the complete sphere=0

=-x*7/6 π r^3d+r/2*4/3 π (r/2)^3d=0

on solving we get,x=r/14

Hope it helps!!!