Question

Copper of fixed volume $V$, is drawn into a 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 will give a straight line?

• A. $\Delta L$ vs. $\frac{1}{L}$
• B. $\Delta L$ vs. $L^2$
• C. $\Delta L$ vs. $\frac{1}{L^2}$
• D. $\Delta L$ vs. $L$

Answer 1

The correct option is B $\Delta L$ vs. $L^2$

As we know,
$\text{Young's modulus}\left(Y\right)=\frac{\text{Stress}}{\text{Strain}}=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}=\frac{FL}{A\Delta L}$
i.e $\Delta L=\frac{FL}{AY}$

Here,
$V=A\times L$ or $A=\frac{V}{L}$
Therefore, $\Delta L=\frac{F{L}^2}{VY}$
$V,F\text{and}Y$ are constant
So, $\Delta L\propto L^2$

Hence graph of $\Delta L$ versus $L^2$ will give a straight line.