Chapter 8, Problem 52P

(II) A sphere of radius $r_1$ has a concentric spherical cavity of radius $r_2$(Fig. 8–40). Assume this spherical shell of thickness $r_1-r_2$ is uniform and has a total mass $M$. Show that the gravitational potential energy of a mass $m$ at a distance $r$ from the center of the shell $r>r_1$ is given by

$\frac{U=-GmM}{r}$

FIGURE 8–40 Problem 60.