Answer
(a) equal to
(b) II
Work Step by Step
(a) We know that $P.E=mgh$. This equation shows that the potential energy depends on the mass and the height. It is given that the balls have the same mass and the same height, hence the change in the gravitational potential energy of ball 1 is equal to the change in gravitational energy of ball 2.
(b) The best explanation is option (II) -- that is, the gravitational potential energy depends only on the mass of the ball and the drop height.