A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(– 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure

Since cavities  are symmetrical w.r.t. O. So the gravitational force at the centre is zero. The radius of the circle  z2+y2=36 is 6.For all points for  r≥6, the body behaves as if whole of the mass is concentrated at the centre. So the gravitational potential is same. Above is true for  z2+y2=4 as well.