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 :

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