Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is $∆\mathrm{l}.$ Which of the following graphs is a straight line?

Young's modulus Y = $\frac{\mathrm{Stress}}{\mathrm{Strain}}$

or Y = $\frac{{\displaystyle \frac{\mathrm{F}}{\mathrm{A}}}}{{\displaystyle \frac{∆\mathrm{l}}{\mathrm{l}}}} = \frac{\mathrm{Fl}}{\mathrm{A}∆\mathrm{l}}$

$\Rightarrow ∆\mathrm{l} = \frac{\mathrm{Fl}}{\mathrm{AY}}$-------(i)

The volume of wire V = Al

or A = $\frac{\mathrm{V}}{\mathrm{l}}$

Substituting the value of A from (ii) in equation (i) 

We get $∆\mathrm{l} \infty {\mathrm{l}}^2$

Hence the graph of $∆$l versus ${\mathrm{l}}^2$ will give a straight line.