The increase in length of a wire on stretching is 0.025%. If its Poisson's ratio is 0.4, then the percentage decrease in diameter is

Options

A. `0.01 %`
B. `0.02 %`
C. `0.03 %`
D. `0.04%`

Answer

To solve the problem, we need to find the percentage decrease in the diameter of a wire when it is stretched, given the increase in length and the Poisson's ratio.

### Step-by-Step Solution:

1. **Understand the given information:**
- Increase in length of the wire (ΔL/L) = 0.025% = 0.00025 (as a decimal)
- Poisson's ratio (σ) = 0.4

2. **Recall the formula for Poisson's ratio:**
\[ \sigma = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} \]
Here, the lateral strain is given by:
\[ \text{Lateral Strain} = \frac{\Delta D/D}{\Delta L/L} \]
Rearranging the formula gives:
\[ \Delta D/D = -\sigma \cdot \frac{\Delta L}{L} \]

3. **Substitute the known values into the formula:**
- We know that ΔL/L = 0.00025 and σ = 0.4.
\[ \Delta D/D = -0.4 \cdot 0.00025 \]

4. **Calculate ΔD/D:**
\[ \Delta D/D = -0.4 \cdot 0.00025 = -0.0001 \]

5. **Convert ΔD/D to percentage:**
To find the percentage decrease in diameter:
\[ \text{Percentage decrease in diameter} = \Delta D/D \times 100 = -0.0001 \times 100 = -0.01\% \]

6. **Final Answer:**
The percentage decrease in diameter is **0.01%**.