Question

Find the potential energy of the gravitational interaction

(a) of two mass points of masses m1 and m2 located at a distance r from each other;

(b) of a mass point of mass m and a thin uniform rod of mass M and length l, if they are located along a straight line at a distance a from each other; also find the force of their interaction.

Answer 1

(a) The gravitational potential due to m1 at the point of location of m2:

(b) Choose the location of the point mass as the origin. Then the potential energy dU of an element of mass dM=M/t dx of the rod in the field of the point mass is

where x is the distance between the element and the point (Note that the rod and the point mass are on a straight line.) If then a is the distance of the nearer end of the rod from the point mass.