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 $$\Delta l.$$  Which of the following graphs is a straight line?

Solution :
Youngs’ modulus is given by $$Y = \frac{{F \times l}}{{A \times \Delta l}}\,.....\left( {\text{i}} \right)$$
As, $$V = A \times l = {\text{constant}}\,.....\left( {{\text{ii}}} \right)$$
From Eqs. (i) and (ii), we get
$$\eqalign{ & Y = \frac{{F \times {l^2}}}{{V \times \Delta l}} \Rightarrow \Delta l = \frac{F}{{V \times Y}} \times {l^2} \cr & \Rightarrow \Delta l \propto {l^2} \cr} $$