What is the limit of Poisson's ratio?
Try it first: pick an option, then read the explanation.
Correct answer: D. None of these
Asked in SSC JE 22/01/2018 (Morning)
Detailed Explanation
Poisson's ratio cannot take just any value; it is bounded by the requirement that elastic constants stay positive.
\( K = \dfrac{E}{3(1 - 2\mu)} \) must be positive, so \( \mu < 0.5 \).
Why “None of these” Is Correct
The upper limit is 0.5 (incompressible material); for normal materials the range is 0 to 0.5. None of 0.1, 0.2 or 0.3 is the limit, so the answer is (d).
| 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. 0.1: 0.1 is a possible value, not the limit.
- B. 0.2: 0.2 is typical for concrete, not the limit.
- C. 0.3: 0.3 is typical for steel, not the limit.
Key Point
0 ≤ μ ≤ 0.5 (theoretical range −1 < μ ≤ 0.5).
Key Concepts for Students
- μ = 0.5 → no volume change under load.
- Negative μ (auxetic materials) exists in special foams.
- K → ∞ as μ → 0.5.
Practice more: this is question 38 in Stress and Strain MCQs – Part 3. Try the whole set and check every answer instantly.