Question

The load versus elongation graph of four wires of equal length of the same material is shown in the figure. The line representing the thinnest wire is

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

The correct option is A $A$

We know that Young's Modulus is given by,
$Y=\frac{\text{Stress}}{\text{Strain}}$
$\Rightarrow Y=\frac{F/A}{\Delta L/L}$
$\Rightarrow \frac{F}{\Delta L}=\frac{YA}{L}$
$\Rightarrow$ Slope $=\frac{YA}{L}$ [from the graph]


For the same material and equal lengths of the wires,
Slope $\propto$ $A$ or $A$ $\propto$ Slope
The wire having minimum area of cross-section (the thinnest wire) will have minimum slope.
From the graph, the slope of the line $A$ is minimum, thus, it represents the thinnest wire.