Introduction:
The buoyant force is the upward force exerted by a fluid on an object submerged in it. It is directly proportional to the acceleration due to gravity, which is approximately 9.8 m/s² on the Earth's surface. This relationship can be explained through Archimedes' principle and the concept of pressure.

Archimedes' Principle:
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. It means that the buoyant force is equal to the weight of the fluid that would occupy the same volume as the submerged object.

The Relationship with Gravity:
The weight of an object is given by the formula: weight = mass × acceleration due to gravity. Since the buoyant force is equal to the weight of the displaced fluid, it can also be expressed as the mass of the fluid × acceleration due to gravity. Therefore, we can conclude that the buoyant force is directly proportional to the acceleration due to gravity.

Explanation:
The relationship between the buoyant force and gravity can be understood by considering the pressure exerted by a fluid. The pressure at any point in a fluid depends on the depth of that point and the density of the fluid. The pressure increases with depth due to the weight of the fluid above it.

When an object is submerged in a fluid, the pressure on its bottom surface is greater than the pressure on its top surface. This pressure difference results in a net upward force known as the buoyant force. The greater the fluid density, the greater the pressure difference and thus the greater the buoyant force.

Since the density of a fluid is independent of the acceleration due to gravity, the buoyant force is solely determined by the weight of the displaced fluid. As gravity provides the weight of the fluid, it indirectly influences the buoyant force acting on an object.

Conclusion:
In conclusion, the buoyant force is directly proportional to the acceleration due to gravity. This relationship is derived from Archimedes' principle and the concept of pressure in a fluid. The greater the acceleration due to gravity, the greater the weight of the displaced fluid, and consequently, the greater the buoyant force on the submerged object.