Introduction:
To find the force of buoyancy on a metallic sphere immersed in water, we need to understand the concept of buoyancy and apply Archimedes' principle.

Archimedes' Principle:
Archimedes' principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle helps us determine the force of buoyancy on the metallic sphere.

Calculating the Volume of the Sphere:
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius. Given that the radius of the metallic sphere is 2 cm, we can substitute this value into the formula to find the volume.

V = (4/3)π(2 cm)³
= (4/3)π(8 cm³)
= (4/3)π(512 cm³)
≈ 2143.67 cm³

Calculating the Buoyant Force:
The buoyant force experienced by the metallic sphere is equal to the weight of the water it displaces. Since the sphere is completely immersed in water, the buoyant force is equal to the weight of the volume of water displaced by the sphere.

Calculating the Weight of Water Displaced:
The weight of the water displaced can be calculated by multiplying the volume of water displaced by the density of water. The density of water is approximately 1 g/cm³ or 1000 kg/m³.

Weight of water displaced = Volume of water displaced × Density of water
≈ 2143.67 cm³ × 1 g/cm³
≈ 2143.67 g

Converting grams to kilograms:
Weight of water displaced = 2143.67 g ÷ 1000
≈ 2.14367 kg

Final Result:
Therefore, the force of buoyancy on the metallic sphere is approximately 2.14367 kg.