For the apparatus in Fig. 6.15, one ball swinging in at a speed of 2vo will not

Question:

For the apparatus in Fig. 6.15, one ball swinging in at a speed of 2vo will not cause two balls to swing out with speeds vo.
(a) Which law of physics precludes this situation from happening: the law of conservation of momentum or the law of conservation of mechanical energy?
(b) Prove this law mathematically.