An aluminium sphere is dipped into water. Which of the following is true ?

Options

A. Buoyancy will be less in water at `0^(@)C` than that in water at `4^(@)C`.
B. Buoyancy will be more in water at `0^(@)C` than that in water at `4^(@)C`.
C. Buoyancy in water at `0^(@)C` will be same as that in water at `4^(@)C`.
D. Buoyancy may be more or less in water at `4^(@)C` depending on the radius of the sphere.

Explanation

To solve the question regarding the behavior of an aluminum sphere when dipped into water, we will analyze the buoyant force acting on the sphere at two different temperatures: 0°C and 4°C.

### Step-by-Step Solution:

1. **Understanding Buoyant Force**:
The buoyant force (F_b) acting on an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. Mathematically, it can be expressed as:
\[ F_b = -\rho \cdot g \cdot V \]
where:
- \( \rho \) = density of the fluid (water in this case),
- \( g \) = acceleration due to gravity (constant),
- \( V \) = volume of the fluid displaced (which is equal to the volume of the submerged part of the sphere).

2. **Density of Water at Different Temperatures**:
- At 0°C, the density of water is approximately 999.8 kg/m³.
- At 4°C, the density of water reaches its maximum, approximately 1000 kg/m³.

3. **Calculating Buoyant Force at 0°C**:
Using the formula for buoyant force at 0°C:
\[ F_{b,0} = -\rho_{0} \cdot g \cdot V \]
where \( \rho_{0} \) is the density of water at 0°C.

4. **Calculating Buoyant Force at 4°C**:
Similarly, for 4°C:
\[ F_{b,4} = -\rho_{4} \cdot g \cdot V \]
where \( \rho_{4} \) is the density of water at 4°C.

5. **Comparing Buoyant Forces**:
Since the density of water at 4°C is greater than that at 0°C, we can conclude:
\[ F_{b,4} > F_{b,0} \]
This means the buoyant force at 4°C is greater than the buoyant force at 0°C.

6. **Conclusion**:
Therefore, the statement that the buoyant force is less in water at 0°C than in water at 4°C is true.

### Final Answer:
The correct statement is that the buoyant force acting on the aluminum sphere when dipped in water at 0°C is less than that at 4°C.

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