`K` is the force constant of a spring. The work done in increasing its extension from `l_1` to `l_2` will be

Options

A. `K(l_2-l_1)`
B. `(K)/(2)(l_2+l_1)`
C. `K(l_2^2-l_1^2)`
D. `(K)/(2)(l_2^2-l_1^2)`

Answer

D

Explanation

At extension `l_1`, the stored energy `=(1)/(2)Kl_1^2`
At extension `l_2`, the stored energy`=(1)/(2)Kl_2^2`
Work done in increasing its extension from `l_1` to `l_2`
`=(1)/(2)K(l_2^2-l_1^2)`