An aluminium sphere is dipped into water at `10^(@)C`. If the water is now heated, the force of buoyancy on the sphere

Options

A. will remain the same
B. will increase
C. will decrease
D. may increase or decrease depending on the initial volume of sphere

Answer

To solve the problem, we need to analyze how the buoyant force acting on the aluminum sphere changes as the temperature of the water increases. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force (Fb) is equal to the weight of the fluid displaced by the object submerged in it.

### Step-by-Step Solution:

1. **Understanding Buoyant Force**:
The buoyant force (Fb) acting on the sphere is given by the formula:
\[ F_b = \rho_w \cdot g \cdot V \]
where:
- \( \rho_w \) = density of water
- \( g \) = acceleration due to gravity (constant)
- \( V \) = volume of the sphere (which is constant since the sphere is not changing)

2. **Effect of Temperature on Water Density**:
The density of water varies with temperature. As water is heated from 10°C:
- From 0°C to 4°C, the density of water increases.
- Above 4°C, the density of water decreases as the temperature increases.

3. **Analyzing the Situation**:
Since the water starts at 10°C and is heated further, we need to focus on the behavior of the water density:
- At 10°C, the density of water is at a certain value.
- As the temperature increases beyond 10°C, the density of water (\( \rho_w \)) will decrease.

4. **Impact on Buoyant Force**:
Since the buoyant force is directly proportional to the density of the water:
- If \( \rho_w \) decreases as the temperature increases, then the buoyant force \( F_b \) will also decrease.

5. **Conclusion**:
Therefore, as the water is heated above 10°C, the buoyant force acting on the aluminum sphere will decrease.

### Final Answer:
The correct option is that the buoyant force will **decrease** as the water is heated above 10°C.