An elastic spring of unstretched length `L` and force constant `K` is stretched by amoun t `x` .It is further stretched by another length `y` The work done in the second streaching is

Options

A. `(1)/(2)kbeta^2`
B. `(1)/(2)k(alpha^2+beta^2)`
C. `(1)/(2)k(alpha+beta)^2`
D. `(1)/(2)kbeta(2alpha+beta)`

Answer

D

Explanation

`U_1=(1)/(2)kalpha^2`,`U_2=(1)/(2)k(alpha+beta)^2`
`W_(1rarr2)=U_2-U_1`
`=(1)/(2)k[(alpha+beta)^2-alpha^2]=(1)/(2)k(2alpha+beta)(beta)`