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

Options

A. Increase in length is inversely proportional to L
B. Increase in length is proportional to area
C. Increase in length is inversely proportional to area
D. Increase in length is proportion to Young's modulus

Explanation

To solve the question regarding the increase in length of an iron wire when a force is applied, we can use the formula for elongation (increase in length) of a wire under tension. The formula is given by:

\[ \Delta L = \frac{F \cdot L}{A \cdot E} \]

Where:
- \(\Delta L\) = increase in length
- \(F\) = applied force
- \(L\) = original length of the wire
- \(A\) = area of cross-section
- \(E\) = Young's modulus of the material

Now, let's analyze the relationship between the increase in length (\(\Delta L\)) and the various parameters involved.

### Step 1: Understand the relationship
From the formula, we can see that the increase in length (\(\Delta L\)) is directly proportional to the applied force (\(F\)). This means that if we increase the force, the increase in length will also increase.

**Hint:** Think about how applying more force affects the stretching of the wire.

### Step 2: Analyze the dependence on original length
The formula also shows that \(\Delta L\) is directly proportional to the original length (\(L\)) of the wire. This means that a longer wire will stretch more than a shorter wire when the same force is applied.

**Hint:** Consider how the length of the wire influences its ability to stretch.

### Step 3: Analyze the dependence on area of cross-section
The increase in length (\(\Delta L\)) is inversely proportional to the area of cross-section (\(A\)). This means that if the area of the wire increases, the increase in length will decrease for the same applied force.

**Hint:** Reflect on how the thickness of the wire affects its stretching.

### Step 4: Analyze the dependence on Young's modulus
The increase in length (\(\Delta L\)) is inversely proportional to Young's modulus (\(E\)). A material with a higher Young's modulus will stretch less under the same force compared to a material with a lower Young's modulus.

**Hint:** Think about how different materials respond to stretching forces.

### Conclusion
Based on the analysis, we can conclude the following relationships:
- Increase in length (\(\Delta L\)) is proportional to the applied force (\(F\)).
- Increase in length (\(\Delta L\)) is proportional to the original length (\(L\)).
- Increase in length (\(\Delta L\)) is inversely proportional to the area of cross-section (\(A\)).
- Increase in length (\(\Delta L\)) is inversely proportional to Young's modulus (\(E\)).

Thus, the correct statement regarding the increase in length of the iron wire when a force is applied is that it is directly proportional to the original length and the applied force, and inversely proportional to the area of cross-section and Young's modulus.

### Final Statement
The correct statement is: "The increase in length is directly proportional to the original length and the applied force, and inversely proportional to the area of cross-section and Young's modulus."