question_answer

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height ft 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:                              [AIPMT (S) 2007]

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

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

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

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

Correct Answer: B

Solution :

Key Idea: Work done is equal to change in energy of body.

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