Question

The stress v/s strain graph of a material is as shown. Find the Young's modulus of the material. 

• A. $10^8\ \text{N/m}^2$
• B. $2\times10^8\ \text{N/m}^2$
• C. $4\times10^8\ \text{N/m}^2$
• D. $3\times10^8\ \text{N/m}^2$

Hint:

In stress–strain graphs, Young’s modulus is simply the slope of the straight-line (elastic) region—pick any clear point to calculate it quickly.

Answer 1

The Correct Option is A

Concept: Young’s modulus $Y$ is defined as the ratio of stress to strain in the linear (elastic) region: \[ Y = \frac{\text{Stress}}{\text{Strain}} \] On a stress–strain graph, Young’s modulus is equal to the slope of the straight-line portion.
Step 1: From the graph, a convenient point on the straight line is: \[ \text{Strain} = 4,\quad \text{Stress} = 4\times10^8\ \text{N/m}^2 \]
Step 2: Calculate the slope of the graph: \[ Y = \frac{4\times10^8}{4} \]
Step 3: \[ Y = 10^8\ \text{N/m}^2 \] Step 4: Hence, the Young’s modulus of the material is: \[ \boxed{10^8\ \text{N/m}^2} \]