If the length of a wire is reduced to half, then it can hold the

Options

A. half load
B. same load
C. double load
D. one fourth load

Explanation

To solve the question, "If the length of a wire is reduced to half, then it can hold the...", we need to understand the relationship between the length of the wire, stress, strain, and the material properties of the wire.

### Step-by-Step Solution:

1. **Understanding Stress and Strain**:
- Stress is defined as the force applied per unit area (σ = F/A).
- Strain is the deformation per unit length (ε = ΔL/L₀).

2. **Young's Modulus**:
- Young's modulus (E) is a measure of the stiffness of a material and is defined as the ratio of stress to strain (E = σ/ε).
- It remains constant for a given material under elastic conditions.

3. **Effect of Length on Stress**:
- When the length of the wire is reduced to half (L = L₀/2), the area of cross-section (A) remains the same.
- If the same load (F) is applied, the stress in the wire will be calculated as:
\[ σ = \frac{F}{A} \]
- Since the area does not change, the stress remains the same.

4. **Effect of Length on Strain**:
- The strain will change because it depends on the original length of the wire. The new strain can be calculated as:
\[ ε = \frac{ΔL}{L} \]
- If the length is halved, the same amount of deformation (ΔL) will result in a higher strain because the denominator (L) is smaller.

5. **Breaking Stress**:
- The breaking stress of the material remains constant regardless of the length of the wire.
- Therefore, the wire can still hold the same load even if its length is halved, as long as it does not exceed the breaking stress.

6. **Conclusion**:
- If the length of a wire is reduced to half, it can still hold the same load, provided that the load does not exceed the breaking stress of the material.

### Final Answer:
If the length of a wire is reduced to half, it can hold the same load as before, provided the load does not exceed the breaking stress of the material.

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