The length of an iron wire is L and area of cross-section is A. The increase in length is `l` on applying the force F on its two ends. Which of the statement is correct

Options

A. increase in length is inversely proportional to its length L
B. Increase in length is proportional to area of cross-section A
C. Increase in length is inversely proportional to A
D. Increase in length is proportional to Young's modulus

Explanation

To solve the problem, we need to analyze the relationship between the elongation of the wire and the parameters given: the original length (L), the area of cross-section (A), the applied force (F), and Young's modulus (Y).

### Step-by-step Solution:

1. **Understanding the Concept**:
The elongation (increase in length) of a wire when a force is applied is described by Hooke's Law, which states that the elongation is directly proportional to the force applied and the original length of the wire, and inversely proportional to the area of cross-section and Young's modulus of the material.

2. **Using the Formula**:
The formula for elongation (ΔL) can be expressed as:
\[ \Delta L = \frac{F \cdot L}{A \cdot Y} \]
where:
- \( \Delta L \) = increase in length (elongation)
- \( F \) = applied force
- \( L \) = original length of the wire
- \( A \) = area of cross-section
- \( Y \) = Young's modulus of the material

3. **Analyzing the Relationship**:
From the formula, we can see that:
- \( \Delta L \) is directly proportional to \( F \) and \( L \).
- \( \Delta L \) is inversely proportional to \( A \) and \( Y \).

4. **Identifying the Correct Statement**:
Since the question asks which statement is correct regarding the increase in length (ΔL), we can conclude:
- As the area of cross-section \( A \) increases, the elongation \( \Delta L \) decreases, indicating that the increase in length is inversely proportional to the area of cross-section.

5. **Conclusion**:
Therefore, the correct statement is that the increase in the length (ΔL) is inversely proportional to the area of cross-section (A).

### Final Answer:
The increase in the length is inversely proportional to the area of cross-section (A).

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