Question

A material shows the following stress-strain data: Stress = 400 MPa at strain = 0.002. Find the modulus of elasticity.

• A. 200 GPa
• B. 100 GPa
• C. 300 GPa
• D. 250 GPa

Hint:

To calculate the modulus of elasticity, divide the stress} by the strain}. Always ensure that your units are consistent — in this case, converting MPa to Pa (Pascals) was necessary to match the SI units.

Answer 1

The Correct Option is A

The modulus of elasticity (E) is a fundamental material property that measures the stiffness of a material. It is defined as the ratio of stress to strain. Mathematically, it is given by the formula: \[ E = \frac{{Stress}}{{Strain}} \] Where: Stress is the force applied per unit area, and Strain is the deformation or displacement of the material per unit length.
In this problem, we are provided with the following values:
- Stress = 400 MPa = \( 400 \times 10^6 \) Pa (since 1 MPa = \( 10^6 \) Pa)
- Strain = 0.002
Substituting these values into the formula for modulus of elasticity: \[ E = \frac{400 \times 10^6}{0.002} \] Performing the calculation: \[ E = 200 \times 10^9 \, {Pa} = 200 \, {GPa} \] Thus, the modulus of elasticity for the material is 200 GPa.
It’s important to note that the modulus of elasticity is a measure of how much a material deforms under stress. A higher value of E indicates that the material is stiffer and resists deformation more effectively. This property is essential in structural engineering and material science, as it helps to predict the behavior of materials under load.