Introduction:
The force of buoyancy is the upward force exerted on an object immersed in a fluid, which opposes the weight of the object. In this case, we need to find the force of buoyancy on a metallic sphere completely immersed in water.

Given:
- Radius of the metallic sphere = 2 cm

Solution:

Step 1: Calculate the volume of the sphere:
The volume of a sphere can be calculated using the formula: V = (4/3)πr³, where r is the radius of the sphere.
Given that the radius of the sphere is 2 cm, we can substitute it into the formula:
V = (4/3)π(2 cm)³ = (4/3)π(8 cm³) = (4/3)π(512 cm³) = 2688/3π cm³

Step 2: Convert volume to liters:
Since the volume of the sphere is given in cubic centimeters (cm³), it is convenient to convert it to liters (L) for easier calculation.
1 liter is equal to 1000 cm³.
Therefore, the volume of the sphere in liters is: (2688/3π) cm³ * (1 L/1000 cm³) = 2.688/3π L

Step 3: Calculate the weight of the water displaced:
The weight of the water displaced by the sphere is equal to the weight of the sphere.
The formula to calculate the weight of an object is: Weight = Mass * Acceleration due to gravity (g)
Since the density of water is 1 g/cm³ and the volume of the sphere is 2.688/3π L, the mass of the water displaced is 2.688/3π kg.
The acceleration due to gravity is approximately 9.8 m/s².
Therefore, the weight of the water displaced is: Weight = (2.688/3π kg) * (9.8 m/s²) = (26.272/3π) N

Step 4: Calculate the force of buoyancy:
The force of buoyancy is equal to the weight of the water displaced.
Therefore, the force of buoyancy on the metallic sphere is (26.272/3π) N.

Conclusion:
The force of buoyancy on the metallic sphere completely immersed in water is (26.272/3π) Newtons.

0.328N