A cable that can support a load W is cut into two equal parts .T he maximum load that can be supported by either part is

Options

A. `(W)/(4)`
B. `(W)/(2)`
C. W
D. 2W

Answer

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the Initial Condition
We have a cable that can support a maximum load \( W \). This means that the breaking force of the cable is \( W \).

**Hint:** Consider what happens to the cable when it is cut into two parts.

### Step 2: Cut the Cable into Two Equal Parts
When the cable is cut into two equal parts, each part will have the same length. However, the area of cross-section of each part remains the same as that of the original cable.

**Hint:** Think about how cutting the cable affects its properties, particularly length and area.

### Step 3: Analyze the Breaking Stress
The breaking stress of a material is defined as the maximum force (load) it can withstand per unit area before failing. The breaking stress (\( \sigma \)) can be expressed as:
\[ \sigma = \frac{F}{A} \]
where \( F \) is the force (load) and \( A \) is the cross-sectional area.

**Hint:** Remember that breaking stress is a material property and does not depend on the length of the cable.

### Step 4: Determine the Maximum Load for Each Part
Since the area of cross-section remains the same and the breaking stress is constant for the material, the maximum load that each part can support will still be \( W \). This is because the breaking stress does not change when the cable is cut.

**Hint:** Consider how the properties of the material influence the load-bearing capacity after cutting.

### Step 5: Conclusion
Therefore, the maximum load that can be supported by either part of the cable after it is cut into two equal parts is still \( W \).

**Final Answer:** The maximum load that can be supported by either part is \( W \).

### Summary of Steps:
1. Understand the initial load capacity \( W \).
2. Cut the cable into two equal parts, noting the unchanged area.
3. Recall the definition of breaking stress.
4. Conclude that the maximum load supported by each part remains \( W \).