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

Step-by-step solution

In the string elastic force is conservative in nature. W =- U Work done by elastic force of string, aligned W &=- ( U _ F - U _ i )= U _ i - U _ F W &= 1 2 k x ²- k 2 ( x + y )² &= 1 2 k x ²- 1 2 k ( x ²+ y ²+2 xy ) &= 1 2 k x ²- 1 2 k y ²- 1 2 kx ²- 1 2 k (2 xy ) &=- k x y - 1 2 k y ² aligned Therefore, the work done against elastic force W _ external =- W = K y 2 (2 x + y )