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 shpere.

Explanation

To solve the question regarding the buoyancy of an aluminum sphere dipped in water at different temperatures, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Buoyancy**:
Buoyancy is the upward force exerted by a fluid on an object submerged in it. The buoyant force (F) can be calculated using the formula:
\[ F = V \cdot \rho \cdot g \]
where \( V \) is the volume of the object, \( \rho \) is the density of the fluid, and \( g \) is the acceleration due to gravity.

2. **Identify Variables**:
- The volume \( V \) of the aluminum sphere remains constant regardless of the temperature of the water.
- The acceleration due to gravity \( g \) is also constant.

3. **Focus on Density**:
The only variable that changes with temperature is the density \( \rho \) of the water. As temperature decreases, the density of water changes:
- At 0°C, the density of water is less than at 4°C.
- Specifically, water reaches its maximum density at 4°C.

4. **Establish the Relationship**:
Since the buoyant force is directly proportional to the density of the fluid, we can express this relationship as:
\[ F \propto \rho \]
Therefore, we can write:
\[ \frac{F_{4°C}}{F_{0°C}} = \frac{\rho_{4°C}}{\rho_{0°C}} \]

5. **Analyze the Densities**:
From the known properties of water:
- \( \rho_{0°C} < \rho_{4°C} \)
This implies that:
\[ F_{0°C} < F_{4°C} \]

6. **Conclusion**:
Since the buoyant force is less at 0°C than at 4°C, we conclude that:
- The buoyancy will be less in water at 0°C than in water at 4°C.

7. **Final Answer**:
Therefore, the correct answer is that buoyancy will be less in water at 0°C than in water at 4°C.