Question

The stress Vs strain graph, for wires of two materials A and B, are as shown in the figure. If ${\gamma }_A$ and ${\gamma }_B$ are the Young's moduli of the two materials, then,

• A. ${\gamma }_A=2{\gamma }_B$
• B. ${\gamma }_B=2{\gamma }_A$
• C. ${\gamma }_A=3{\gamma }_B$
• D. ${\gamma }_B=3{\gamma }_A$

Answer 1

The correct option is C ${\gamma }_A=3{\gamma }_B$

The Young's modulus is given by,

$\gamma =\frac{\text{Tensile Stress}}{\text{Tensile Strain}}$

So, the slope of stress Vs strain graph will be equal to the Young's modulus of the material.

$\Rightarrow {\gamma }_A=\tan {60}^{\circ }=\sqrt{3}$

And, ${\gamma }_B=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$

$\therefore {\gamma }_A=3{\gamma }_B$

Hence, $\left(C\right)$ is the correct answer.