Fundamentals of stress and strain: Which statement below is incorrect? Select the single wrong definition among linear strain, Poisson’s ratio, volumetric strain, and bulk modulus.

Introduction / Context:
Engineering mechanics relies on precise terminology. Confusing basic definitions of strain measures and elastic moduli leads to wrong designs. This question checks conceptual clarity on linear strain, Poisson’s ratio, volumetric strain, and bulk modulus.

Given Data / Assumptions:

• Small deformations (engineering strain) are considered.
• Isotropic, homogeneous materials in the elastic range.
• Standard sign conventions (tension positive).

Concept / Approach:
Recall the standard definitions:Linear (longitudinal) strain ε = ΔL / L.Poisson’s ratio ν = − (lateral strain / longitudinal strain); the magnitude equals lateral/longitudinal.Volumetric strain ε_v = ΔV / V.Bulk modulus K = hydrostatic (volumetric) stress / volumetric strain.Young’s modulus E, not K, is the ratio of linear stress to linear strain in uniaxial loading.

Step-by-Step Solution:

Verification / Alternative check:
Elasticity relations: σ = E * ε (uniaxial); p = K * ε_v (hydrostatic). These confirm the mismatch in option (d).

Why Other Options Are Wrong:
They are not wrong; (a), (b), and (c) are standard textbook definitions.“None of these is wrong” is invalid because (d) is incorrect.

Common Pitfalls:
Mixing up E and K; treating Poisson’s ratio without noting that lateral strain is of opposite sign; confusing volumetric and linear strains.

Final Answer:

Bulk modulus is the ratio of linear stress to linear strain.