If longitudinal strain for a wire is 0.03 and its Poisson's ratio is 0.5, then its lateral strain is

Options

A. 0.003
B. 0.0075
C. 0.015
D. 0.4

Explanation

To solve the problem, we need to find the lateral strain using the given longitudinal strain and Poisson's ratio. Here’s a step-by-step solution:

### Step 1: Understand the relationship between longitudinal strain, lateral strain, and Poisson's ratio.
Poisson's ratio (σ) is defined as the negative ratio of lateral strain (ε_lat) to longitudinal strain (ε_long):
\[ \sigma = -\frac{\text{lateral strain}}{\text{longitudinal strain}} \]

### Step 2: Rearrange the formula to find lateral strain.
From the definition, we can rearrange the formula to express lateral strain in terms of Poisson's ratio and longitudinal strain:
\[ \text{lateral strain} = -\sigma \times \text{longitudinal strain} \]

### Step 3: Substitute the given values into the formula.
We are given:
- Longitudinal strain (ε_long) = 0.03
- Poisson's ratio (σ) = 0.5

Substituting these values into the rearranged formula:
\[ \text{lateral strain} = -0.5 \times 0.03 \]

### Step 4: Calculate the lateral strain.
Now, performing the multiplication:
\[ \text{lateral strain} = -0.015 \]

### Step 5: Interpret the result.
Since strain is typically expressed as a positive value, we can state that the magnitude of the lateral strain is 0.015.

### Final Answer:
The lateral strain is 0.015.

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