K is the force constant of a spring. The work donein 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)/(2)(l_(2)^(3)-l_(1)^(3))`

Answer

B

Explanation

`u_(1)=(1)/(2)K l_(1)^(2) and u_(2) =(1)/(2)Kl_(2)^(2)`
`u=(1)/(2) K(l_(2)^(2) -l_(1)^(2))`