Poisson’s ratio is defined as the ratio of:A. Longitudinal stress and longitudinal strainB. Longitudinal stress and lateral stress C. Lateral stress and longitudinal stressD. Lateral stress and lateral strain

Poisson's Ratio:
Poisson’s ratio (ν\nu) is a dimensionless quantity that describes the relationship between the lateral strain and the longitudinal strain in a material under stress. It is defined as the ratio of the lateral strain (ϵlateral\epsilon_{\text{lateral}}) to the longitudinal strain (ϵlongitudinal\epsilon_{\text{longitudinal}}).
Mathematically:
ν=−ϵlateralϵlongitudinal\nu = -\frac{\epsilon_{\text{lateral}}}{\epsilon_{\text{longitudinal}}}
Here:
• Lateral strain (ϵlateral\epsilon_{\text{lateral}}): The change in dimension perpendicular to the direction of the applied force divided by the original dimension in that direction.
• Longitudinal strain (ϵlongitudinal\epsilon_{\text{longitudinal}}): The change in dimension along the direction of the applied force divided by the original dimension in that direction.
• The negative sign accounts for the fact that lateral strain is typically opposite in direction to the longitudinal strain.
Explanation of Options:
1. Option A: Longitudinal stress and longitudinal strain
This defines the modulus of elasticity (Young's modulus), not Poisson’s ratio.
2. Option B: Longitudinal stress and lateral stress
This is incorrect as Poisson’s ratio involves strain, not stress.
3. Option C: Lateral stress and longitudinal stress
This is also incorrect because Poisson’s ratio relates strain, not stress.
4. Option D: Lateral strain and longitudinal strain
This is correct because Poisson’s ratio is the ratio of lateral strain to longitudinal strain.
Final Answer:
The correct option is D. Lateral strain and longitudinal strain.