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) \[36\sqrt{7}\]   

B) \[4\sqrt{5}\]                      

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, network does in the process is W = potential energy stored in the spring                      + loss of potential energy of mass \[=20\times {{10}^{10}}=2\times {{10}^{11}}N/{{m}^{2}}\]