Problem $4$: Evaluate the gravitational potential energy between two $5\mathrm{.}00-kg$ spherical steel balls separated by a center$-$to$-$center distance of $15\mathrm{.}0$ cm $.$ Then:

Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast will they be traveling upon impact. Each sphere has a radius of $5\mathrm{.}10$ cm $.$