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I'm assuming no gravity (and that at least one ball is moving). Do you have a proof for your assertion?
Sure.
If the center of gravity moves, it moves with the velocity v. So it will be in the position r+v*t after some time t. Now it's at the position r. A different position of gravity (mass) center means different position. For the whatever finite t.
In the case when the gravity center doesn't move, you can divide the composition into two sub-compositions, where both gravity centers do move. If only one had moved, then the combined gravity center would move and we would have the solved case above.
But if both gravity centers move, they can either move apart a... (read more)