Step 1: Concept Overview:
Poisson's ratio quantifies the Poisson effect, where a material contracts perpendicularly to its stretching direction.
Step 2: Core Formula:
When stretched lengthwise, a material undergoes a longitudinal strain (\(\epsilon_{\text{long}}\)). This stretching causes thinning in the transverse direction, resulting in a lateral strain (\(\epsilon_{\text{lat}}\)).
Poisson's ratio (\(u\)) is the negative ratio of lateral to longitudinal strain:
\[ u = - \frac{\epsilon_{\text{lat}}}{\epsilon_{\text{long}}} = - \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} \]
The negative sign ensures that stretching (positive longitudinal strain) leads to contraction (negative lateral strain), and vice versa. The answer choices relate to the absolute values of the ratio.
Step 3: Explanation:
By definition, Poisson's ratio is lateral strain divided by longitudinal strain. It concerns strains, not stresses, eliminating options (C) and (D). Option (B) is the inverse of the correct definition. Option (A) accurately states the definition as the ratio of lateral strain to longitudinal strain.
Step 4: Conclusion:
Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain.