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

To find the Young's modulus of the material, we need to understand that Young's modulus is defined as the ratio of stress to strain in the linear elastic portion of the material's stress-strain curve. It is given by the formula:

\(E = \frac{\text{Stress}}{\text{Strain}}\)

From the given stress-strain graph, we need to determine the gradient of the linear portion. The graph shows stress on the vertical axis (in N/m²) and strain on the horizontal axis.

Examining the graph:

• At strain = 1, stress = \(1 \times 10^8\ \text{N/m}^2\)
• At strain = 2, stress = \(2 \times 10^8\ \text{N/m}^2\)

Using these points, the Young's modulus \(E\) is calculated as follows:

\(E = \frac{2 \times 10^8 - 1 \times 10^8}{2 - 1} = 1 \times 10^8\ \text{N/m}^2\)

Therefore, the Young's modulus of the material is \(1 \times 10^8\ \text{N/m}^2\), which matches the first option provided.

Correct Answer: \(1 \times 10^8\ \text{N/m}^2\)