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

B

Explanation

Work done is equal to change in energy of body. Situation is shown in figure. When mas `m` falls vertically on spring. Then spring is compressed by distance `d`. Hence, net work done in the process is
`W` = potential energy stroed in the spring
`+` loss of potential energy of mass
=`mg(h + d) - (1)/(2) kd^2`.