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. Work done during the second stretching is

Options

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

Answer

d

Explanation

According to the question
In the first condition
`W_(1) = (1)/(2) kx^(2)`
In the second condition
`W_(2) = (1)/(2) k (x + y)^(2)`
Work for x to y expansion
`= (1)/(2) k (x + y)^(2) - (1)/(2) kx^(2)`
`= (1)/(2) k [x^(2) + y^(2) + 2xy - x^(2)]`
`= (1)/(2) k[y^(2) + 2xy]`
`= (1)/(2) ky [y + 2x]`