The Poisson’s ratio for a metal is 0.25. If lateral strain is 0.0125, the longitudinal strain will be

The correct answer/option is 0.05.

Step-by-Step Explanation:

1. Understanding Poisson's Ratio:
Poisson's ratio (denoted by the Greek letter $\nu$ or $\sigma$) is a dimensionless constant that describes the deformation of a material perpendicular to the direction of an applied load. It is defined as the ratio of lateral strain to longitudinal strain:
$\text{Poisson's ratio}=\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$

2. Identifying the Given Values:
From the problem statement, we are given:
• Poisson's ratio ($\nu$) = $0.25$
• Lateral strain = $0.0125$

3. Calculating the Longitudinal Strain:
We can rearrange the formula for Poisson's ratio to solve for the longitudinal strain:
$\text{Longitudinal Strain}=\frac{\text{Lateral Strain}}{\text{Poisson's ratio}}$

Substituting the given values into the rearranged equation:
$\text{Longitudinal Strain}=\frac{0.0125}{0.25}$

Simplifying the fraction:
$\text{Longitudinal Strain}=0.05$

Thus, the longitudinal strain will be 0.05.