Question

The increase in length of a wire on stretching is \(0.05%\). If its Poisson’s ratio is 0.4, then its diameter is reduced by

• A. \(0.02%\)
• B. \(0.1%\)
• C. \(0.01%\)
• D. \(0.2%\)

Hint:

Poisson’s ratio always links lateral and longitudinal strain directly.

Answer 1

The Correct Option is A

Step 1: Poisson’s ratio definition.
\[ \mu = \frac{\text{lateral strain}}{\text{longitudinal strain}} \]
Step 2: Given longitudinal strain.
\[ \text{Longitudinal strain} = 0.05% = 0.0005 \]
Step 3: Calculating lateral strain.
\[ \text{Lateral strain} = \mu \times \text{longitudinal strain} \] \[ = 0.4 \times 0.0005 = 0.0002 \]
Step 4: Converting to percentage.
\[ 0.0002 \times 100 = 0.02% \]
Step 5: Conclusion.
The diameter is reduced by 0.02%.