# Archimedes Principle

If you submerge any solid object in water, it appears to lose weight. If we go swimming, we also feel a little weightless in the water. The reason for this is that liquids exert an upward force to objects submerged in them. This is known as thrust and is a consequence of the difference in pressure a liquid exerts at different heights. As we submerge an object (Considering it is fully submerged) deeper into a liquid, the pressure exerted by the liquid keeps on increasing but the thrust force remains same.

## Archimedes Principle Definition

The value of this thrust force is given by the Archimedes principle which was discovered by Archimedes of Syracuse of Greece. When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of liquid displaced by it.Archimedes’ principle states that “the upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.

### Archimedes Principle Class 9

If you look at the figure, the weight due to gravity is opposed by the thrust provided by the fluid. The object inside the liquid only feels the total force acting on it as the weight. Because the actual gravitational force is decreased by the liquid’s upthrust, the object feels as though its weight is reduced. The apparent weight is thus given by:

Apparent weight= Weight of object (in air) – Thrust force (buoyancy)

Archimedes principle tells us that this loss of weight is equal to the weight of liquid the object displaces. If the object has a volume of V, then it displaces a volume V of the liquid when it is fully submerged. If only a part of the volume is submerged, the object can only displace that much of liquid.

## Archimedes principle Formula

In simple form, the Archimedes principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:

Fb = ρ x g x V.

where,
Fb is the buoyant force.
ρ is the density the fluid
V is the submerged volume
g is the acceleration due to gravity.

## Archimedes principle Derivation

The mass of the liquid displaced is.

$Mass$ = $Density~ × ~Volume$ = $ρ~×~V$

This is because density (ρ) is defined as

$Density,ρ$ = $\frac{Mass}{Volume}$ = $\frac{M}{V}$

Thus the weight of that displaced liquid is:

$Weight$ = $Mass~ ×~ Acceleration~ due~ to~ gravity$

$W$ = $M~×~g$ = $ρ~×~V~×~g$

Thus from Archimedes principle, we can write:

Apparent loss of weight = weight of water displaced = ρ×V×g

Thus the Thrust force is,

$Thrust$ = $ρ~×~V~×~g$

Where, $ρ$ = density of liquid

$V$ = volume of liquid displaced

The thrust force is also called the buoyant force because it is responsible for objects to float. Thus, this equation is also called the law of buoyancy.

## Archimedes Principle Experiment

You can try an Archimedes principle experiment at home. Take a mug filled with water to the brim and place it in an empty bowl. Now take any solid object you like and measure its weight using a spring balance. Note this down. Keep the object attached to the spring balance and submerge it in the water. Just make sure the spring balance is not submerged. Now, note down the weight shown by the spring balance. You will notice that it is less. Some water will be displaced into the bowl. Collect this water and weigh it. You will find that the weight of the water will be exactly equal to the loss of weight of the object!

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