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

Loss in P.E. `=` gain in the spring energy `mg(h+d)=(1)/(2)kd^2`
net work done `=mg(h+d)-(1)/(2)kd^2`