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

`w_1 =(1)/(2) kx^2`
`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)kpx^2+y^2+2xy]-(1)/(2)kx^2`
`=(1)/(2)k[x^2+y^2+2xy-x^2]`
`=(1)/(2) k[y^2+2xy]`
`=(1)/(2)k y [y+2x]` .