Question

Under the elastic limit, Poisson's ratio is:

• A. The ratio of the lateral strain to the longitudinal strain
• B. The ratio of the longitudinal strain to the lateral strain
• C. The ratio of the lateral stress to the longitudinal stress
• D. The ratio of the longitudinal stress to the lateral stress

Hint:

Remember "lateral over longitudinal". When you pull something (longitudinal), the sides (lateral) get thinner. Poisson's ratio quantifies this effect. Most materials have a Poisson's ratio between 0 and 0.5.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Poisson's ratio is a measure of the "Poisson effect," which is the phenomenon where a material tends to contract in directions perpendicular to the direction of stretching.
Step 2: Key Formula or Approach:
When a material is stretched along its length, it experiences a longitudinal strain (\(\epsilon_{\text{long}}\)). As a result of this stretching, it becomes thinner in the transverse directions, experiencing a lateral strain (\(\epsilon_{\text{lat}}\)).
Poisson's ratio (\(\nu\)) is defined as the negative of the ratio of lateral strain to longitudinal strain:
\[ \nu = - \frac{\epsilon_{\text{lat}}}{\epsilon_{\text{long}}} = - \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} \]
The negative sign indicates that a positive longitudinal strain (stretching) results in a negative lateral strain (contraction), and vice versa. The options refer to the ratio of the magnitudes.
Step 3: Detailed Explanation:
Based on the definition, Poisson's ratio is the ratio of lateral strain to longitudinal strain. It relates strains, not stresses. Therefore, options (C) and (D) are incorrect. Option (B) is the reciprocal of the correct definition. Option (A) correctly identifies it as the ratio of lateral strain to longitudinal strain.
Step 4: Final Answer:
Poisson's ratio is the ratio of the lateral strain to the longitudinal strain.