Question

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
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 1

Work done is equal to change in energy of body.
Situation is done in the figure. When mass `m` falls vertically on spring then spring is compresed by distance `d`.
Hence net work done in the process is
`W = ` Potential energy stored in the spring
`+` Loss of potential energy
` = mg (h + d) - (1)/(2) kd^(2)`