Question

Which of the following material has bigger Young's modulus?

• A. A
• B. B
• C. C
• D. D

Hint:

On a strain–stress graph, the stiffer the material, the flatter the line and the larger the Young’s modulus.

Answer 1

The Correct Option is D

Concept:

Young’s modulus \(Y\) is defined as: \[ Y = \frac{\text{Stress}}{\text{Strain}} \]
On a strain vs stress graph: \[ \text{slope} = \frac{\text{Strain}}{\text{Stress}} = \frac{1}{Y} \]
Hence, larger Young’s modulus corresponds to a smaller slope.
Step 1: Analyze the given graph. The graph plots:
Stress on the \(x\)-axis
Strain on the \(y\)-axis Thus, the slope of each line is: \[ \text{slope} = \frac{\text{Strain}}{\text{Stress}} \]
Step 2: Compare slopes of lines A, B, C, and D. From the diagram: \[ \text{Slope: } A>B>C>D \]
Step 3: Relate slope to Young’s modulus. Since: \[ Y \propto \frac{1}{\text{slope}} \] The material with the smallest slope has the largest Young’s modulus. \[ \Rightarrow \text{Material D has the largest Young’s modulus} \]