Question

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

• A. $Y_B=2Y_A$
• B. $Y_A=Y_B$
• C. $Y_B=3Y_A$
• D. $Y_A=3Y_B$

Answer 1

The correct option is D $Y_A=3Y_B$

Young's modulus is defined as
$Y=\frac{\text{Stress}}{\text{Strain}}$
$\therefore$ Young's modulus is slope of stress strain curve.
$\frac{Y_A}{Y_B}=\frac{\tan {\theta }_A}{\tan {\theta }_B}=\frac{\tan {60}^{\circ }}{\tan {30}^{\circ }}=\frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=3Y_A=3Y_B$
Hence, the correct answer is option (d).