A force of 400 kg. weight can break a wire. The force required to break a wire of double the area of cross-section will be

Options

A. 800 kg -wt
B. 200 kg wt
C. 1600 kg wt
D. 100 kg wt

Explanation

To solve the problem, we need to determine the force required to break a wire that has double the area of cross-section compared to an original wire that can be broken by a force of 400 kg weight.

### Step-by-Step Solution:

1. **Understanding the Relationship Between Force and Area**:
- The force required to break a wire is related to its cross-sectional area. Specifically, the breaking force (F) is directly proportional to the area (A) of the wire.
- Mathematically, we can express this as:
\[ F \propto A \]
- This means if we double the area, the force required to break the wire will also double.

2. **Identifying the Given Values**:
- The original wire can be broken by a force of 400 kg weight. We denote this as \( F_1 = 400 \, \text{kg} \).
- The area of the original wire is \( A_1 \).
- The area of the new wire, which is double the original area, is \( A_2 = 2A_1 \).

3. **Setting Up the Proportional Relationship**:
- Since the force is proportional to the area, we can write:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]
- Here, \( F_2 \) is the force required to break the new wire with area \( A_2 \).

4. **Substituting the Known Values**:
- We know \( A_2 = 2A_1 \), so we can substitute this into our equation:
\[ \frac{400}{A_1} = \frac{F_2}{2A_1} \]

5. **Solving for \( F_2 \)**:
- Cross-multiplying gives us:
\[ 400 \cdot 2A_1 = F_2 \cdot A_1 \]
- Dividing both sides by \( A_1 \) (assuming \( A_1 \neq 0 \)):
\[ F_2 = 800 \, \text{kg} \]

6. **Conclusion**:
- The force required to break a wire of double the area of cross-section is 800 kg weight.

### Final Answer:
The force required to break a wire of double the area of cross-section is **800 kg weight**.