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

Answer 1

Answer: (A)

$mg(h+d)-\frac{1}{2}kd^2$

Answer 2

Net work done $=$ work done by gravitational force $+$ work done by spring force
$=m g(h+d)-\frac{1}{2} K d^{2}$