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

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 :

 Work done is equal to change in energy of body. Situation is shown in the 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 \[=mg(h+d)-\frac{1}{2}k{{d}^{2}}\]