Question

Figure beside represents strain versus stress graph for four materials $A, B, C$ and $D$. Which material has maximum Young's modulus?

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Hint:

Always check which quantity is on each axis. For a strain vs stress graph, smaller slope $\Rightarrow$ larger Young’s modulus.

Answer 1

The Correct Option is A

Concept: Young’s modulus $Y$ is defined as: \[ Y=\frac{\text{Stress}}{\text{Strain}} \] If a graph is plotted with strain on the y-axis and stress on the x-axis, then: \[ \text{slope}=\frac{\text{strain}}{\text{stress}}=\frac{1}{Y} \] Hence, larger the slope, smaller the Young’s modulus, and vice versa.
Step 1: From the given graph: - Line $A$ has the smallest slope - Lines $B$, $C$, and $D$ have progressively increasing slopes
Step 2: Since Young’s modulus is inversely proportional to the slope of the strain–stress graph, \[ Y \propto \frac{1}{\text{slope}} \]
Step 3: Therefore, the material with the least slope will have the maximum Young’s modulus. Step 4: Material $A$ has the least slope. Conclusion: \[ \boxed{\text{Material } A \text{ has maximum Young's modulus}} \]