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) K (x + y)^(2)`

Answer

C

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)`