When body is subjected to three mutually perpendicular stresses of equal intensity, the ratio of direct stress to the corresponding volumetric strain is known as
- AYoung’s Modulus
- BModulus of Rigidity
- CBulk ModulusCorrect
- DPoisson’s Ratio
Solution
Concept
Bulk modulus is direct stress divided by volumetric strain under equal stress in all three directions.
Formula
K = σ / ev ; K = E / [3(1 - 2μ)]
Step-by-step solution
1. The body has equal stress σ in all three perpendicular directions. 2. Because of this, its volume changes. Volumetric strain ev = ΔV/V. 3. The ratio σ / ev is defined as the bulk modulus K. 4. Answer is (C).
Explanation
When equal stress acts on a body from all three directions (like water pressure), only its volume changes. The ratio of this stress to the volumetric strain is called the bulk modulus K. It is related to E and μ by K = E / [3(1 - 2μ)].
Why the other options are wrong
A: Young's modulus uses linear strain, not volumetric strain. B: Modulus of rigidity uses shear stress and shear strain. D: Poisson's ratio is a ratio of two strains, not stress to strain.
Shortcut
Volumetric strain always goes with bulk modulus.
Common mistake
Choosing Young's modulus because the question says "direct stress".
Correct answer: C) Bulk Modulus