11. The following problem is from the 1946 "Olympic" examination of Moscow State University (see Fig. 14-36):
spherical hollow is made in a lead sphere of radius R, such that its
surface touches the outside surface of the lead sphere and passes
through its center.
The mass of the sphere before hollowing was M.
With what force, according to the law of universal gravitation, will
the hollowed lead
sphere attract a small sphere of mass m, which
lies at a distance d from the center of the lead sphere on the straight
line connecting the centers of the spheres and of the hollow?