question_answer

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)  \[mg\left( h-d \right)+\frac{1}{2}k{{d}^{2}}\]

Correct Answer: B

Solution :

                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\[=mg(h+d)-\frac{1}{2}k{{d}^{2}}\]