A load w is suspended from a wire of length `l` and area of cross-section A. Change in length of the wire is say `Deltal`. Change in length `Deltal` can be increased to two times by increasing

Options

A. w by two times
B. l by two times
C. A by two times
D. A by four times

Answer

To solve the problem, we need to understand how the change in length (Δl) of a wire is affected by various parameters when a load (W) is applied. The relationship between the change in length of a wire and the parameters involved can be derived from Hooke's Law and the formula for stress and strain in materials.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The change in length (Δl) of a wire under a load can be described by the formula:
\[ \Delta l = \frac{W \cdot l}{A \cdot Y} \]
where:
- \( W \) = Load applied
- \( l \) = Original length of the wire
- \( A \) = Cross-sectional area of the wire
- \( Y \) = Young's modulus of the material (a constant for a given material)

2. **Doubling the Change in Length**:
To increase the change in length (Δl) to two times its original value, we can manipulate the parameters in the equation. We want:
\[ 2\Delta l = \frac{W \cdot l}{A \cdot Y} \]

3. **Identifying Parameters to Change**:
To achieve this, we can consider the following parameters:
- **Increase the Load (W)**: If we double the load, the change in length will also double.
- **Increase the Length (l)**: If we double the length of the wire, the change in length will also double.
- **Decrease the Cross-sectional Area (A)**: If we reduce the area, the change in length will increase.
- **Young's Modulus (Y)**: This is a material property and cannot be changed for a given material.

4. **Conclusion**:
From the analysis, we can conclude that to increase the change in length (Δl) to two times, we can either:
- Increase the load (W) to two times.
- Increase the length (l) to two times.
- Decrease the area (A) to half.

Therefore, the parameters that can be increased to achieve this are:
- Load (W)
- Length (l)
- Cross-sectional area (A) can be decreased.

### Final Answer:
To double the change in length (Δl), you can increase:
- The load (W) to two times.
- The length (l) to two times.
- Decrease the cross-sectional area (A) to half.