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)

Answer: Option (D)

Solution:

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
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