Modulus of rigidity is expressed as:
Try it first: pick an option, then read the explanation.
Correct answer: C. shear stress / shear strain
Asked in SSC JE (CWC & MES) 2011
Detailed Explanation
Each elastic modulus is a ratio of a stress to its matching strain within the elastic limit.
Why “shear stress / shear strain” Is Correct
The modulus of rigidity G is shear stress / shear strain.
| Modulus | Definition | Relation |
|---|---|---|
| Young's modulus E | Normal stress / normal (linear) strain | — |
| Modulus of rigidity G (shear modulus) | Shear stress / shear strain | E = 2G(1 + μ) |
| Bulk modulus K | Hydrostatic stress / volumetric strain | E = 3K(1 − 2μ) |
Why the Other Options Are Wrong
- A. compressive stress / compressive strain: Compressive stress/strain gives Young's modulus (in compression).
- B. tensile stress / tensile strain: Tensile stress/strain gives Young's modulus E.
- D. stress / volumetric strain: Stress/volumetric strain gives the bulk modulus K.
Key Point
E = σ/ε, G = τ/φ, K = σ/εv.
Key Concepts for Students
- E = 2G(1 + μ) = 3K(1 − 2μ).
- Units of G: N/mm².
- Shear strain φ is measured in radians.
Practice more: this is question 29 in Principal Stress and Principal Planes MCQs – Part 2. Try the whole set and check every answer instantly.