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:                                                                                                                                  

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