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 true but Reason is false.
D. If both Assertion and Reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason given in the problem.

### 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 Cylinder**:
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 cylinder.

3. **Doubling the Radius**:
If the radius of the cylindrical wire is doubled, the new radius \( r' \) becomes:
\[ r' = 2r \]
The new area of cross-section \( A' \) will be:
\[ A' = \pi (r')^2 = \pi (2r)^2 = \pi \cdot 4r^2 = 4\pi r^2 \]
Thus, the area becomes four times the original area.

4. **Calculating New Stress**:
If the same force \( F \) is applied to the wire with the new area \( A' \), the new stress \( \sigma' \) can be calculated as:
\[ \sigma' = \frac{F}{A'} = \frac{F}{4\pi r^2} \]
Since the original stress \( \sigma \) was:
\[ \sigma = \frac{F}{\pi r^2} \]
We can see that:
\[ \sigma' = \frac{F}{4\pi r^2} = \frac{1}{4} \cdot \frac{F}{\pi r^2} = \frac{\sigma}{4} \]

5. **Conclusion**:
This shows that when the radius is doubled, the stress actually decreases to one-fourth of the original stress, not increases to four times. Therefore, the assertion is false.

6. **Evaluating the Reason**:
The reason states that by doubling the radius, the area of cross-section becomes four times. This statement is true. However, the assertion that the wire can bear four times the stress is false.

### Final Answer:
- The assertion is **false**.
- The reason is **true**.
- Therefore, the correct conclusion is that the assertion is incorrect while the reason is correct.