On a horizontal surface, a steel ring is lying flat. The steel ring has a mass of "M" and a radius of "$a$". A small lead ball with a mass of "m" is placed at a distance of "z" above the center of the ring, along a vertical line that passes through the center of the ring, and is perpendicular to its plane. Taking the potential energy to be zero when the two objects are infinitely separated, derive an expression for the gravitational potential energy "U" of this system.