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)/(2)(l_(2)+l_(1))`
B. `(k)/(2)(l_(2)^(2)-l_(1)^(2))`
C. `k(l_(2)^(2)-l_(1)^(2))`
D. `k(l_(2)-l_(1))`

Answer

B

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))`