If a wire is extended to a new length , the L, the work done is

Options

A. `(YA)/(l)(l-l)`
B. `(YA)/(l)(l-l)^2`
C. `1/2(YA)/(l)(l-l')^2 `
D. `(YA)/(l)(l-l)^2`

Answer

C

Explanation

`Y = (F//A)/((Deltal)/(l))`
`therefore F = (YA)/(l) * Delta l = k * Deltal`
Force `prop` extension
If the extension is x , work done in extending by dx
dW = kx dx `" " therefore W = (1)/(2) k * x^(2)`
If x is l' - l , W = `(1)/(2) k (l' -l)^(2)`
i.e. work done is `(1)/(2) (YA)/(l) (l-l')^(2)`