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

Options

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

Explanation

To solve the problem regarding the buoyancy of an aluminum sphere when dipped in water at different temperatures, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Buoyancy**:
- Buoyancy is the upward force exerted by a fluid on an object submerged in it. This force is equal to the weight of the fluid displaced by the object.

2. **Volume of the Sphere**:
- The volume \( V \) of the aluminum sphere can be calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
- Here, \( r \) is the radius of the sphere.

3. **Buoyant Force Calculation**:
- The buoyant force \( F_b \) acting on the sphere when it is submerged in water is given by:
\[ F_b = \rho_w \cdot g \cdot V \]
- Where \( \rho_w \) is the density of water, \( g \) is the acceleration due to gravity, and \( V \) is the volume of the sphere.

4. **Density of Water at Different Temperatures**:
- The density of water varies with temperature. It reaches its maximum value at 4 degrees Celsius.
- At temperatures above or below 4 degrees Celsius, the density of water \( \rho \) is less than \( \rho_w \) at 4 degrees Celsius.

5. **Comparing Buoyant Forces**:
- When the sphere is submerged in water at 0 degrees Celsius, the density of water \( \rho_{0°C} \) is less than the density of water at 4 degrees Celsius \( \rho_{4°C} \).
- Therefore, the buoyant force at 0 degrees Celsius will be:
\[ F_{b, 0°C} = \rho_{0°C} \cdot g \cdot V \]
- And the buoyant force at 4 degrees Celsius will be:
\[ F_{b, 4°C} = \rho_{4°C} \cdot g \cdot V \]

6. **Conclusion**:
- Since \( \rho_{4°C} > \rho_{0°C} \), it follows that:
\[ F_{b, 4°C} > F_{b, 0°C} \]
- Thus, the buoyancy will be greater in water at 4 degrees Celsius compared to water at 0 degrees Celsius.

7. **Choosing the Correct Option**:
- Based on the analysis, the correct statement is:
- Option 1: Buoyancy will be less in water at 0 degrees Celsius than that in water at 4 degrees Celsius.

### Final Answer:
The correct option is **Option 1**: Buoyancy will be less in water at 0 degrees Celsius than that in water at 4 degrees Celsius.