# Buoyant Force formula

Last updated on July 7th, 2023 at 10:11 am

In this post, our topic of discussion is the

Buoyant Force formula. As we go through it here, we will use this formula to solve a sample numerical as well.Remember that, the

upward buoyant forcecaused byBuoyancy is equal to the weight of the displaced fluid.

## Buoyant Force Formula

Note: **Upward buoyant force **caused by** Buoyancy = the weight of the displaced fluid.****The magnitude of Buoyant force is expressed with the formula F _{b} = ρ g V**

Here

**ρ**is the density of the fluid, V is the volume of the fluid displaced, g is the acceleration due to gravity

**Read our tutorial on Buoyancy.**

**Numerical Problem** based on Buoyant Force formula (with solution)

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.

**SOLUTION**

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.

**Buoyant force** – concepts

- Consider a body immersed in a liquid. Two forces act on it simultaneously.
- The weight (W) of the body is acting vertically down at its center of gravity (C.G).
- The upthrust or buoyant force (FB) is 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.