A, lift the ball to the suspension point o of the rope and let it fall freely. At t 1, the rope is just tight. At this time, the gravity on the ball is greater than the tension of the rope, and the ball accelerates downward. When the tension of the rope is greater than gravity, the ball begins to slow down. At t2, the tension of the rope reaches the maximum, and the ball moves to the lowest point at zero speed, so at t 1 and t4, the rope is just right.

At times b, t2 and t5, the ball reaches its lowest point, and its velocity and kinetic energy are zero. Therefore, B is correct.

C, t3, the ball falls, the momentum direction is downward, t4, the ball rises, the momentum direction is upward, and the momentum at the two moments is different. So, C is wrong.

D, because the tension of the elastic rope does work on the ball, the mechanical energy of the ball is not conserved. So, d is wrong.

So choose B.