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

Answer 1

Answer: (B)

When a ball of mass $m$ is dropped from a height
h and the spring is compressed by d, then loss in potential energy of mass m is $mg(h+d)$ while gain in elastic potential energy o f the spring will be $\frac{1}{2}k{d}^2$
Net workdone in the process $W=mg(h+d)-\frac{1}{2}k{d}^2$