An elastic spring 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 

Options

A. `1/2 ky^2`
B. `1/2 k(x^2 + y^2)`
C. `1/2 k(x + y)^2`
D. `1/2 ky (2x + y)`

Answer

D

Explanation

Potential energy stored in the spring when it is further extended by y is `U_2 = 1/2 k(x + y)^2`
`:.`Work done = `U_2 - U_1 = 1/2 k(x + y)^2 - 1/2 kx^2`
`= 1/2 ky (2x + y)`.