Which expression represents Archimedes' buoyant force on a submerged object?

• A. F_b = ρ_fluid g / V_submerged
• B. F_b = m g
• C. F_b = ρ_fluid V_total g
• D. F_b = ρ_fluid V_submerged g

Answer: (D)

Buoyant force comes from the pressure differences in the fluid surrounding a submerged object, and the net upward force equals the weight of the fluid that would occupy the submerged volume. So the force is determined by how much fluid is displaced: F_b = ρ_fluid g V_submerged.

This means if the object is fully under water, V_submerged is the object's total volume, giving F_b = ρ_fluid g V_total. If only part of the object is submerged, the buoyant force is smaller because less fluid is displaced. The object’s own weight m g is not the buoyant force, and using the total volume instead of the submerged volume would incorrectly assume full immersion. Dividing density by a volume would not produce a correct force either.