# An elastic string of unstretched length 𝐿 and force constant 𝑘 is stretched by a small length 𝑥. It is further stretched by another small length 𝑦. The work done in the second stretching is

Question: An elastic string of unstretched length 𝐿 and force constant 𝑘 is stretched by a small length 𝑥. It is further stretched by another small length 𝑦. The work done in the second stretching is

(A) $\dfrac{1}{2}ky^{2}$

(B) $\dfrac{1}{2}k\left( x^{2}+y^{2}\right)$

(C) $\dfrac{1}{2}k\left( x+y\right) ^{2}$

(D) $\dfrac{1}{2}ky\left( 2x+y\right)$