Q. 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) $mg(h + d) + \frac{1}{2}kd^{2}$
B) $mg(h + d) - \frac{1}{2}kd^{2}$
C) $mg(h - d) - \frac{1}{2}kd^{2}$
D) $mg(h - d) + \frac{1}{2}kd^{2}$
Explanation
(b) Situation is shown in figure. When mass m falls vertically on spring, then spring is compressed by distance d.
[image:6_image102.jpeg]
Hence, net work done in the process is
W=Potential energy stored in the spring
+Loss of potential energy of mass
=$mg(h + d) - \frac{1}{2}kd^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.