Within the elastic limit of a material, the modulus of elasticity is the ratio of:
Try it first: pick an option, then read the explanation.
Correct answer: C. stress to strain
Asked in SSC JE 23/03/2021 (Evening)
Detailed Explanation
Hooke's law says stress is proportional to strain in the elastic range. The constant of proportionality is the modulus of elasticity.
\[ E = \frac{\sigma}{\varepsilon} = \frac{P/A}{\delta L / L} = \frac{PL}{A\,\delta L} \]
Why “stress to strain” Is Correct
So E is the ratio of stress to strain. It has the units of stress because strain is dimensionless.
Why the Other Options Are Wrong
- A. area to strain: Area divided by strain has no meaning as a material constant.
- B. stress to area: Stress divided by area has wrong units.
- D. strain to stress: Strain ÷ stress is the inverse (compliance).
Key Point
E = σ/ε (slope of the straight part of the stress–strain curve).
Key Concepts for Students
- Steel E ≈ 200 GPa; concrete ≈ 25–35 GPa.
- Higher E = stiffer material.
- Elongation δ = PL/AE.
Practice more: this is question 9 in Stress and Strain MCQs – Part 1. Try the whole set and check every answer instantly.