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A ball with mass \( m \) is attached to the end of a rod of mass \( M \) and length \( l \). The other end of the rod is pivoted, so that the ball can move in a vertical circle. The rod is held in the horizontal position as shown in the figure and then given just enough a downward push, so that the ball swings down and just reaches the vertical upward position having zero speed there. Now, answer the following questions.
The change in potential ènergy of the system (ball + rod) is
(a) \( m g l \)
(b) \( (M+m) g l \)
(c) \( \left(\frac{M}{2}+m\right) g l \)
(d) \( \frac{(M+m)}{2} g l \)
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