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)`

Explanation

Situation is shown in figure. When mass `m` falls vertically on spring , then spring is compressed by dictance `d`.

Hence, net force work done in the process is
`W = ` potential energy stored in the spring
`+` loss of potantial energy of mass
`= mg (h+d) - (1)/(2) k d^(2)`