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 Yound's modulus.

Answer

To solve the problem, we need to analyze the relationship between the increase in length (l) of an iron wire when a force (F) is applied, considering its original length (L), cross-sectional area (A), and Young's modulus (Y).

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Stress (σ)** is defined as the force (F) applied per unit area (A):
\[ \sigma = \frac{F}{A} \]
- **Strain (ε)** is defined as the change in length (l) per unit original length (L):
\[ \epsilon = \frac{l}{L} \]

2. **Applying Hooke's Law**:
- According to Hooke's Law, stress is proportional to strain:
\[ \sigma = Y \cdot \epsilon \]
- Substituting the definitions of stress and strain into Hooke's Law gives:
\[ \frac{F}{A} = Y \cdot \frac{l}{L} \]

3. **Rearranging the Equation**:
- Rearranging the equation to find the increase in length (l):
\[ l = \frac{F \cdot L}{A \cdot Y} \]

4. **Analyzing the Relationships**:
- From the equation \( l = \frac{F \cdot L}{A \cdot Y} \), we can derive the following relationships:
- The increase in length (l) is **directly proportional** to the applied force (F).
- The increase in length (l) is **directly proportional** to the original length (L).
- The increase in length (l) is **inversely proportional** to the cross-sectional area (A).
- The increase in length (l) is **inversely proportional** to Young's modulus (Y).

5. **Evaluating the Statements**:
- **Statement 1**: Increase in length is inversely proportional to its length (L) - **Incorrect**.
- **Statement 2**: Increase in length is proportional to the cross-sectional area (A) - **Incorrect**.
- **Statement 3**: Increase in length is inversely proportional to A - **Correct**.
- **Statement 4**: Increase in length is proportional to Young's modulus (Y) - **Incorrect**.

### Conclusion:
The only correct statement is that the increase in length (l) is inversely proportional to the cross-sectional area (A).