An elastic spring of unstretched length L and spring constant K is stretched by a small length x. It is further stretched by another small length y. the work done in second stretcing is

Options

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

Answer

d

Explanation

P.E stored in the spring when it is stretched by a length x is `U_(1) = (1)/(2) Kx^(2)`
when it is stretched by a further distance y, the P.E
`(1)/(2) K (x + y)^(2)`
`:.` work done `= U_(2) - U_(1) = (1)/(2) K [(x + y)^(2) - x^(2)]`
`= (1)/(2) k [x^(2) + y^(2) + 2xy - x^(2)]`
`W = (1)/(2) Ky (2x + y)`