Assertion : A solid object of iron is dipped in water, both are at same temperature of `2^(@)C`. If the temperature of water is increased by `2^(@)C`, then the buoyancy force action of the object will increase.
Reason : If we increase the temperature of water from `2^(@)C " to " 4^(@)C`, then density of water will increase. Ignore expansion of solid sphere.

Options

A. If both Assertion and Reason are correct 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 Assertion is false but Reason is true.

Answer

To solve this problem, we need to analyze both the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that when a solid object of iron is dipped in water at 2°C and the temperature of the water is increased by 2°C, the buoyant force acting on the object will increase.

2. **Buoyant Force Formula**:
The buoyant force (B) acting on an object submerged in a fluid is given by Archimedes' principle:
\[ B = \rho \cdot V \cdot g \]
where:
- \( \rho \) is the density of the fluid (water in this case),
- \( V \) is the volume of the fluid displaced (equal to the volume of the object submerged),
- \( g \) is the acceleration due to gravity.

3. **Initial Conditions**:
- Initially, the water is at 2°C. Let the density of water at 2°C be \( \rho_2 \).
- The buoyant force at this temperature can be expressed as:
\[ B_{\text{initial}} = \rho_2 \cdot V \cdot g \]

4. **Final Conditions**:
- After increasing the temperature, the water is now at 4°C. Let the density of water at 4°C be \( \rho_4 \).
- The buoyant force at this temperature can be expressed as:
\[ B_{\text{final}} = \rho_4 \cdot V \cdot g \]

5. **Density Comparison**:
- It is known that water reaches its maximum density at 4°C. Therefore, the density of water at 4°C (\( \rho_4 \)) is greater than the density of water at 2°C (\( \rho_2 \)):
\[ \rho_4 > \rho_2 \]

6. **Conclusion on Buoyant Force**:
- Since \( \rho_4 > \rho_2 \), it follows that:
\[ B_{\text{final}} > B_{\text{initial}} \]
Thus, the buoyant force acting on the object increases when the temperature of the water is raised from 2°C to 4°C.

7. **Understanding the Reason**:
The reason states that increasing the temperature of water from 2°C to 4°C results in an increase in the density of water. This is true because water has its maximum density at 4°C.

8. **Final Assessment**:
- Both the assertion and the reason are true.
- The reason correctly explains the assertion.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.