Poisson's ratio for a linear elastic, homogeneous and isotropic material:
Try it first: pick an option, then read the explanation.
Correct answer: C. remains constant throughout
Asked in SSC JE 15/11/2022 (Shift 3)
Detailed Explanation
Homogeneous: same properties at every point. Isotropic: same properties in every direction. Linear elastic: stress proportional to strain.
Why “remains constant throughout” Is Correct
With all three properties, the ratio of lateral to longitudinal strain is a fixed material constant. It remains constant regardless of the stress level (within the elastic range), location or direction.
| Material | Poisson's ratio μ |
|---|---|
| Cork | ≈ 0 |
| Concrete | 0.15 – 0.20 |
| Cast iron | 0.21 – 0.26 |
| Steel | 0.27 – 0.30 |
| Copper | ≈ 0.33 |
| Rubber | 0.45 – 0.50 |
For isotropic materials μ cannot exceed 0.5; above that the volume would decrease under tension.
Why the Other Options Are Wrong
- A. varies linearly with stress: In the linear elastic range μ does not change with stress.
- B. is not the same for tension and compression: For linear elastic isotropic materials μ is the same in tension and compression.
- D. is in the range 0 to 1: For isotropic materials μ lies between 0 and 0.5, not up to 1.
Key Point
μ is a material constant (0 to 0.5 for isotropic materials).
Key Concepts for Students
- μ = −lateral strain / longitudinal strain.
- Steel ≈ 0.3, concrete ≈ 0.15–0.2.
- Two of E, G, K, μ are independent.
Practice more: this is question 5 in Stress and Strain MCQs – Part 1. Try the whole set and check every answer instantly.