Question

The stress versus strain graph for the wire of two materials $P$ and $Q$ are shown in the figure. If the $Y_P$ and $Y_Q$ are the Young's Modulus of the materials, then

• A. $Y_P=3Y_Q$
• B. $Y_P=\sqrt{3}{Y}_Q$
• C. $Y_P=Y_Q$
• D. $Y_Q=\sqrt{3}{Y}_P$

Answer 1

The correct option is B $Y_P=\sqrt{3}{Y}_Q$

We know, $\text{Young's Modulus}\left(Y\right)=\frac{\text{Stress}}{\text{Strain}}=$Slope of graph
$\therefore Y=\tan \theta$


So, $Y_P=\tan {45}^{\circ }=1...\left(1\right)$
and $Y_Q=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}...\left(2\right)$
Dividing equation $\left(1\right)$ by $\left(2\right)$, we get
$\frac{Y_P}{Y_Q}=\frac{1}{1}\times \sqrt{3}$
$\Rightarrow Y_P=\sqrt{3}{Y}_Q$