The modulus of elasticity of a material is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/06/2024 (9 am–11 am)
Detailed Explanation
Hooke's law says that, up to the limit of proportionality, stress is directly proportional to strain. The constant of proportionality is the modulus of elasticity (Young's modulus) E.
\[ \sigma = E\,\varepsilon \;\Rightarrow\; E = \frac{\sigma}{\varepsilon}\quad(\text{N/mm}^2) \]
Why “only defined in the linearly elastic region” Is Correct
The ratio σ/ε is constant only on the straight, initial part of the stress–strain curve. Beyond that the curve bends, the ratio keeps changing and a single E no longer exists. So E is defined only in the linearly elastic region, as the slope of that straight portion.
Why the Other Options Are Wrong
- A. having the same unit as that of strain: Strain has no unit; E has the unit of stress (N/mm², GPa).
- C. not referred to as Young's modulus: The modulus of elasticity is exactly what is called Young's modulus.
- D. equal to the slope of the strain–stress curve: E is the slope of the stress–strain curve (σ on the y-axis), not the strain–stress curve.
Key Point
E = σ/ε, valid only in the linear elastic range; unit of stress.
Key Concepts for Students
- For mild steel E ≈ 2 × 10⁵ N/mm² (200 GPa).
- Beyond the proportional limit, secant or tangent moduli are used instead of E.
- A higher E means a stiffer material (less strain for the same stress).
Practice more: this is question 2 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.