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 ($E$) is a measure of a material's stiffness. It describes how well a material resists being stretched or compressed. Mathematically, it is defined as: $$E = \frac{\sigma}{\epsilon}$$ where $\sigma$ is Stress (force per unit area) and $\epsilon$ is Strain (deformation).

Step 1: Understand Material Behavior. Materials with a high Young's modulus are "stiff"—they require a significant amount of force to produce even a small change in shape. Conversely, materials with a low Young's modulus are "flexible" or "elastic" and deform easily under small forces.
Step 2: Evaluate the Categories. Generally, materials follow a hierarchy of stiffness:

• High $E$: Ceramics, Diamond, and Metals (like Steel).
• Low $E$: Polymers, Rubbers, and biological tissues.

Step 3: Conclusion based on stiffness. If Material D is identified as having the largest Young's modulus, it means it is the stiffest material in the group. It undergoes the least amount of proportional deformation when subjected to the same load as materials A, B, or C.

$$\Rightarrow \text{Material D has the largest Young’s modulus}$$