If the Young's modulus of a material is twice its modulus of rigidity, its Poisson's ratio is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 24/01/2018 (Morning)
Detailed Explanation
Use the relation between E, G and μ.
\[ E = 2G(1 + \mu) \;\Rightarrow\; 2G = 2G(1 + \mu) \;\Rightarrow\; \mu = 0 \]
Why “None of these” Is Correct
Poisson's ratio comes out as zero, which is not among (a)–(c), so the answer is (d) None of these.
Disputed answer: the commission's revised key marked (a) −1. That value would need E = 0 (since E = 2G(1 + μ)), which is impossible for a real material. Mathematically, μ = 0, so we give (d).
| Relation | Formula |
|---|---|
| Young's modulus and rigidity | E = 2G(1 + μ) |
| Young's modulus and bulk modulus | E = 3K(1 − 2μ) |
| All three moduli | E = 9KG/(3K + G) |
| Poisson's ratio | μ = (3K − 2G)/(6K + 2G) |
Only two elastic constants are independent for a homogeneous, isotropic, linearly elastic material.
Why the Other Options Are Wrong
- A. −1: Marked in the revised key, but μ = −1 would make E = 0.
- B. −0.5: μ = −0.5 would make E = G.
- C. 0.5: μ = 0.5 would make E = 3G.
Key Point
E/G = 2(1 + μ): E = 2G → μ = 0; E = 3G → μ = 0.5.
Key Concepts for Students
- For steel, E/G ≈ 2.6.
- Cork has μ ≈ 0, so E ≈ 2G.
- Theoretical range for isotropic materials: −1 < μ ≤ 0.5.
Practice more: this is question 33 in Stress and Strain MCQs – Part 3. Try the whole set and check every answer instantly.