Assertion If radius of cylinderical wire is doubled, then this wire can bear four times stress.
Reason By doubling the radius, area of cross-section will become four times.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is false but Reason is true.
D. If both Assertion and Reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding Stress**:
Stress (σ) is defined as the force (F) applied per unit area (A) of the material. Mathematically, it is expressed as:
\[ \sigma = \frac{F}{A} \]

2. **Area of Cross-Section of a Cylindrical Wire**:
The area of cross-section (A) of a cylindrical wire is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the wire.

3. **Doubling the Radius**:
If the radius of the cylindrical wire is doubled (i.e., \( r \) becomes \( 2r \)), we can calculate the new area of cross-section:
\[ A' = \pi (2r)^2 = \pi (4r^2) = 4\pi r^2 = 4A \]
This shows that the area of cross-section becomes four times the original area.

4. **Effect on Stress**:
Since stress is inversely proportional to the area (keeping the force constant), we can express this relationship as:
\[ \sigma' = \frac{F}{A'} = \frac{F}{4A} = \frac{1}{4} \cdot \frac{F}{A} = \frac{\sigma}{4} \]
This indicates that the new stress (σ') is one-fourth of the original stress (σ).

5. **Conclusion**:
The assertion states that if the radius of the cylindrical wire is doubled, then the wire can bear four times the stress. However, our calculations show that the stress actually decreases to one-fourth of its original value. Therefore, the assertion is **false**.

6. **Reason Analysis**:
The reason states that by doubling the radius, the area of cross-section will become four times. This is indeed true, as we calculated earlier.

### Final Answer:
- The assertion is false, and the reason is true. Therefore, the correct conclusion is that the assertion does not hold true based on the reasoning provided.