Which of the following statements is correct with respect to the modulus of rigidity?
Try it first: pick an option, then read the explanation.
Correct answer: A. It is the ratio of shear stress to shear strain.
Asked in SSC JE 15/11/2022 (Shift I)
Detailed Explanation
The modulus of rigidity G (also called the shear modulus) is the elastic constant for shear deformation.
Why “It is the ratio of shear stress to shear strain.” Is Correct
G = τ/φ, the ratio of shear stress to shear strain. It is related to E and Poisson's ratio by E = 2G(1 + μ).
| 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
- B. It depends only on the modulus of elasticity and has no relation with Poisson's ratio.: G depends on both E and μ: G = E/(2(1 + μ)).
- C. It is also known as the bulk modulus of elasticity.: The bulk modulus K relates hydrostatic stress to volumetric strain.
- D. It is not known as the shear modulus of elasticity.: It is exactly what is called the shear modulus.
Key Point
G = τ/φ = E/(2(1 + μ)).
Key Concepts for Students
- For μ = 0.3, G ≈ 0.385E.
- Unit of G is N/mm² (same as stress).
- G is used in torsion: T/J = Gθ/L.
Practice more: this is question 4 in Principal Stress and Principal Planes MCQs – Part 1. Try the whole set and check every answer instantly.