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

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 $\frac{1}{2}kd^{2}$
Net workdone in the process $W=mg (h+d)-\frac{1}{2} kd^{2}$