The system composed of two balls and rods, A and A, only works by gravity, and the mechanical energy of the system is conserved, so A is correct;

B. At the beginning, the ball B is stationary and the speed of B is zero. When A landed, B's speed was also zero. So in the whole process of A sliding to the ground, B accelerates first and then decelerates. During the whole movement of B, only the lamp pole does work for B. Therefore, the lamp pole does positive work for B first and then negative work, so B is wrong.

C, when ball A landed, the speed was vertical downward, which was not zero, while the speed of ball B was zero, so the speed of two balls when ball A landed was not equal, so C was wrong;

When balls D and A land, B's speed is zero. In the whole process, the mechanical energy of the system is conserved, which is obtained by the law of conservation of mechanical energy: mAgL= 12mAv2.

Solution: v=2gL, so D is correct;

Therefore: ad.