# Archimedes Principle Formula

Fundamental to fluid mechanics Archimedes’ principle is a fundamental law of physics. Archimedes’ principle indicates that the increasing buoyant force that is applied on a body submerged in a liquid, whether partially or fully immersed, is equivalent to the mass of the fluid that the form displaces. The object will sink, if the mass of the water displaced is less than the weight of the body, otherwise, the body will float, with the weight of the water displaced equivalent to the mass of the object.

When a body is totally or partly submerged in a fluid it experiences buoyancy (upward force) that is equivalent to the mass of the fluid displaced.
Archimedes Principle Formula is known as

$F=\rho&space;gV$

Where, Buoyant force of a given body = F,
Volume of the displaced fluid = v
acceleration due to gravity = g

As we see that density ρρ = ρf – ρg. Here ρf is the density of the fluid and ρg is the density of the body.
Thus, the formula can also be articulated as

$F=(\rho_{f}-\rho_{g})gV$

Archimedes principle formula is helpful in finding the buoyant force, the volume of displaced body, the density of fluid or density of body if some of these numerics are known.

Archimedes Principle Problems Solved Examples

Underneath are given some problems based on Archimedes principle.

Problem 1: A ball of mass 2 kg that has a diameter of 50 cm falls in the pool. Compute its buoyant force and volume of water displaced.

Known:

Mass of water, m = 2 kg,

Diameter of ball, d = 0.5 m r = 0.25 m

$Volume\,&space;of\,&space;sphere\,&space;V=\frac{4}{3}\;\Pi&space;r^{3}=\frac{4}{3}\;\Pi\;&space;0.25^{3}$

$Hence\,&space;the\,&space;density\,&space;is\,&space;given\,&space;by\,&space;\rho&space;=\frac{Mass}{Volume}=\frac{2kg}{0.0208m^{3}}$

The force is given by F = mg. Hence buoyant force is

F = 2 kg × 9.8 m/s2 = 19.6 N

The Archimedes formula is given by F = ρρ g Vdisp

$Hence\,&space;the\,&space;volume\,&space;of\,&space;displaced\,&space;fluid\,&space;is\,&space;V_{disp}=\frac{F}{\rho&space;g}=\frac{19.6}{96\times&space;9.8}=0.0208\,m^{3}$

Hence volume of given body=Volume of displaced liquid

Problem 2: Calculate the buoyant force acting on it, if a stone of mass 250 g is thrown in water?