The upward buoyant force caused by Buoyancy is equal to the weight of the displaced fluid.
Buoyant Force formula
The magnitude of Buoyant force is expressed with the formula Fb = ρ g V where ρ is the density of the fluid, V is the volume of the fluid displaced, g is the acceleration due to gravity
Numerical Problem based on Buoyant Force formula
The densities of water and ice are 1 g cm-3 and 0⋅917 g cm-3. Find the fraction of an iceberg floating above the water surface and the fraction below it.
Let V = the total volume of the iceberg.
V1 = volume of the iceberg above the water surface
∴ V − V1 = volume of the iceberg below the water surface that provides the upthrust (buoyant force) to balance the weight of the entire iceberg while the iceberg floats.
By the law of floatation weight of the iceberg = weight of the water displaced by the immersed part of the iceberg.
V × 0.917 × g = (V − V1) × 1 × g
V1 = (1 − 0.917) V
V1/V = 0.083/1 = 1/12
Thus, 1/12th part of the total volume of the iceberg floats above the water surface.
∴ 11/12th part of the iceberg is submerged in water.
It means most of the iceberg is beneath the water.
Brief revision about buoyant force
Consider a body immersed in a liquid. Two forces act on it simultaneously. They are the weight (W) of the body acting vertically down at its center of gravity (C.G).
The upthrust or buoyant force (FB), equal to the weight of the liquid displaced, acting vertically upwards. The point where the total upthrust due to the liquid displaced by the immersed part of the body acts is called the center of buoyancy.
The weight of the body acts vertically down whereas the buoyant force acts vertically up.