A wire is stretched by one mm by a force of 1 kN. The work done is stretching the wire is

Options

A. 5 ergs
B. 5 Joules
C. 0.5 ergs
D. 0.5 Joules

Answer

To solve the problem of calculating the work done in stretching a wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Force (F) = 1 kN = 1000 N (since 1 kN = 1000 N)
- Stretching amount (x) = 1 mm = 1 × 10^-3 m (since 1 mm = 0.001 m)

2. **Use the Formula for Work Done**:
- The work done (W) in stretching a wire can be calculated using the formula:
\[ W = \frac{1}{2} F x \]
- Here, F is the force applied, and x is the extension (stretching amount).

3. **Substitute the Values into the Formula**:
- Substitute F = 1000 N and x = 1 × 10^-3 m into the formula:
\[ W = \frac{1}{2} \times 1000 \, \text{N} \times 1 \times 10^{-3} \, \text{m} \]

4. **Calculate the Work Done**:
- Calculate the multiplication:
\[ W = \frac{1}{2} \times 1000 \times 10^{-3} = \frac{1000}{2} \times 10^{-3} = 500 \times 10^{-3} = 0.5 \, \text{J} \]

5. **Final Answer**:
- The work done in stretching the wire is:
\[ W = 0.5 \, \text{J} \]

### Conclusion:
The work done in stretching the wire is **0.5 Joules**.

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