Example: A point mass m = 51 x 10^{2} kg is placed at the center of the base of a uniform hemisphere of mass M = 115 x 10^{8} kg and radius R = 163 m. What is the potential energy of interaction due to gravitational force? Solution: Consider an elementary section of thickness dr at a distance r from the center O of the hemisphere as shown in the figure. Let dM be the mass of this elementary section. Then, Using equation (G.17) for a distributed mass system, the potential V at the point O is given by The potential energy of interaction due to gravitational force is the product of the potential V and the mass m. Thus, Now substituting m = 51 x 10^{2} kg, M = 115 x 10^{8} kg and radius R = 163 m in the expression obtained above, the potential energy of interaction U =  36.00 J.
