The longitudinal extention of any elastic material is very small.In order to have an appericiable change ,the material must be in the form of

Options

A. long thick wire
B. short thick wire
C. long thin wire
D. short thin wire

Explanation

To solve the problem, we need to understand the relationship between the longitudinal extension of an elastic material and its dimensions. The formula we will use is:

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

where:
- \(\Delta L\) is the change in length (longitudinal extension),
- \(F\) is the applied force,
- \(L\) is the original length of the material,
- \(A\) is the cross-sectional area,
- \(Y\) is the Young's modulus of the material.

### Step-by-Step Solution:

1. **Understanding Longitudinal Extension**:
The longitudinal extension (\(\Delta L\)) of an elastic material is defined as the change in length when a force is applied. According to the formula, \(\Delta L\) is directly proportional to the original length (\(L\)) and the applied force (\(F\)), and inversely proportional to the cross-sectional area (\(A\)) and Young's modulus (\(Y\)).

2. **Analyzing the Formula**:
From the formula, we can see that for a given force, if the area \(A\) is large, the change in length \(\Delta L\) will be small. Conversely, if the length \(L\) is large, the change in length \(\Delta L\) can be significant.

3. **Condition for Appreciable Change**:
The question states that the longitudinal extension is very small. To achieve an appreciable change in length, we need to maximize the effect of the length while minimizing the effect of the area. This can be achieved by using a material that is long and thin.

4. **Conclusion**:
Therefore, in order to have an appreciable change in length for a small longitudinal extension, the material must be in the form of a long wire. This configuration allows the effect of the length to dominate over the effect of the cross-sectional area.

5. **Final Answer**:
The material must be in the form of a long wire.