Question

The Poisson’s ratio of a material is 0.4. If the force is applied to a wire of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is:

• A. 3%
• B. 2.5%
• C. 1%
• D. 0.5%

Hint:

The Poisson’s ratio relates the lateral strain to the longitudinal strain in a material.

Answer 1

The Correct Option is B

We are given the Poisson's ratio \( \nu = 0.4 \), and the decrease in cross-sectional area is 2%. 
The percentage change in length \( \Delta L \) can be calculated using the following relation:

\[ \text{Poisson's ratio} = \frac{\text{Lateral strain}}{\text{Longitudinal strain}} = \frac{-\Delta A / A}{\Delta L / L} \]

The lateral strain is the decrease in area, so:

\[ \frac{\Delta A}{A} = -2\% \]

Thus, the longitudinal strain (percentage change in length) is:

\[ \frac{\Delta L}{L} = -\frac{\Delta A / A}{\nu} = \frac{-(-2\%)}{0.4} = 2.5\% \]

Final Answer: 2.5%