the problem 15 H.C.Verma from gravitation is

 

A thin spherical shell having uniform density is cut in two parts by a plane and kept separated. The point A is the center of the plane section of the first partand B of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.

Gravitational field at any point inside a thin spherical shell is always zero.

Hence, if a shell is cut by a plane it means that the centers A and B of the two cut portions of the shell which were earlier coinciding must have equal gravitational field due to the shells to which they belong

thus, gravitational field at A = Gravitationl field at B

further, the field due to two parts are equal and opposite so that when the two portions are combined together the resultant gravitational field at these points will again be zero.