A metallic sphere of mass 2 . 0 kg and volume ` 2 . 5 xx 10 ^(-4) m^(3)` is completely immersed in water. Find the buoyant force exerted by water on the sphere
Density of water ` = 1000 kg// m^(3)`

Options

A. 2 . 45 N
B. 0 . 25 N
C. 20 N
D. 30 N

Explanation

To find the buoyant force exerted by water on the metallic sphere, we can use Archimedes' principle, which states that the buoyant force (upthrust) is equal to the weight of the fluid displaced by the object.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the sphere, \( m = 2.0 \, \text{kg} \)
- Volume of the sphere, \( V = 2.5 \times 10^{-4} \, \text{m}^3 \)
- Density of water, \( \rho_w = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

2. **Calculate the Mass of the Displaced Water:**
The mass of the displaced water can be calculated using the formula:
\[ m_d = V \times \rho_w \]
Substituting the values:
\[ m_d = 2.5 \times 10^{-4} \, \text{m}^3 \times 1000 \, \text{kg/m}^3 \]
\[ m_d = 2.5 \times 10^{-1} \, \text{kg} = 0.25 \, \text{kg} \]

3. **Calculate the Weight of the Displaced Water:**
The weight of the displaced water (which is equal to the buoyant force) can be calculated using the formula:
\[ F_b = m_d \times g \]
Substituting the values:
\[ F_b = 0.25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ F_b = 2.45 \, \text{N} \]

4. **Conclusion:**
The buoyant force exerted by water on the sphere is:
\[ F_b = 2.45 \, \text{N} \]