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