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. $mg(h+d)+\frac{1}{2}k{d}^2$
• B. $mg(h+d)-\frac{1}{2}k{d}^2$
• C. $mg(h-d)-\frac{1}{2}k{d}^2$
• D. $mg(h-d)+\frac{1}{2}k{d}^2$

Answer 1

Answer: (B)

Work done is equal to change in energy of body.
Situation is shown in figure. When mass $m$ falls vertically on spring, then spring is compressed by distance $d$.
Hence, net work done in the process is
$W=$ potential energy stored in the spring $+$ loss of potential energy of mass
$=mg(h+d)-\frac{1}{2}k{d}^2$