Two small metal spheres, each of mass m, are attached to the lower ends of two long insulated strings of negligible mass as shown. Each string is length, l. The spheres are pulled apart until each string makes an angle "theta" with the horizontal. A charge of +q is placed on one sphere and a charge of -q is placed on the other. The spheres are then released from rest, make a perfectly elastic collision, neutralize their charges and rebound (bounce apart). Find the maximum angle each string makes relative to the vertical after the collision.
The following link is a copy of the problem with solution and diagram provided by my professor.
The Attempt at a Solution
I do not believe this problem is solvable without knowing the radius of the hanging masses. However my professor and her colleague disagreed. They claim U=-kQq/r will always give you the correct value for potential energy between two charges regardless where zero potential is defined. It is my understanding that equation  is only useful when we have an initial and a final value of r such that neither is zero. It stands to reason that equation  must also be used in a similar manner where r-initial and r-final are clearly defined.
It appears to me that U=kq^2/r will only tell us how much work is done by the charges when we bring one of them from infinity to r distance away from the other. It does not tell us how much work one will do to the other if we are to release them while they are r distance apart. I was told I was wrong in thinking this way. Am I missing something here? Please enlighten me.
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