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

Options

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

Answer

C

Explanation

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