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 vartical circle. The rod is held in the horizontal position as shown in 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 energy of the system (ball+rod) is

Options

A. `mgl`
B. `(M+m)gl`
C. `((M)/(2)+m)gl`
D. `((M+m))/(2)gl`

Answer

C

Explanation

`DeltaU=DeltaU_(rod)+DeltaU_(ball)`
`=Mg((1)/(2))+mgl`
`=((M)/(2)+m)gl`