Four particles, each of mass m, are situated at the vertices of a regular tetrahedron of side a. Find the gravitational force exerted on any one of the particles by the other three. Three uniform rigid spheres of mass M and radius a are placed on a horizontal table and are pressed together so that their centres are at the vertices of an equilateral triangle.
A fourth uniform rigid sphere of mass M and radius a is placed on top of the other three so that all four spheres are in contact with each other. Find the gravitational force exerted on the upper sphere by the three lower ones.