A vertical spring with force constant `k` is fixed on a table. A ball of mass `m` at a height `h` above the free upper end of the spring falls vertically on the spring , so that the spring is compressed by a distance `d`. The net work done in the process is

Options

A. `mg(h+d)-(1)/(2)Kd^(2)`
B. `mg(h-d)-(1)/(2)Kd^(2)`
C. `mg(h-d)+(1)/(2)Kd^(2)`
D. `mg(h+d)+(1)/(2)Kd^(2)`

Answer

A

Explanation

As the spring is compressed through a distance `(d)` therefore, total energy supplied by the ball `=mg(h+d)`, being the potential energy of the ball, figure.
Now, `P.E.` of compressed spring `=(1)/(2)Kd^(2)`
`:.` Net work done in the process
`W=mg(h+d)-(1)/(2)Kd^(2)`