What Is Archimedes' Principle( Definition, Formula, Derivation, Application and Experiment)

Archimedes' Principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.

The value of thrust force is given by the Archimedes law 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.



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 terms, Archimedes' Law states that the boiling force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:

Archimedes Principle Derivation:

The mass of the liquid displaced is.

The thrust force is also called the buoyant force because it is responsible for floating objects. Thus, this equation is also called the law of buoyancy.Archimedes Principle Applications

Following are the applications of Archimedes principle:

Submarine:

The reason why submarines are always under water is because they have a component called ballast tank which allows the water to enter the submarine in its position as the weight of the submarine is greater than the buoyant force.

Hot-air balloon:

The reason why a hot-air balloon rises and floats in mid-air because the buoyant force of the hot-air balloon is less than the surrounding air. When the buoyant force of the hot-air balloon is more, it starts to descend. This is done by varying the quantity of hot air in the balloon.

Hydrometer:

A hydrometer is an instrument used for measuring the relative density of liquids. The hydrometer consist of lead shots which makes them float vertically on the liquid. The lower the hydrometer sinks, the lesser the density of the liquid.

Archimedes Principle Experiment

You can try an Archimedes principle experiment at home.

1. Take a mug filled with water to the brim and place it in an empty bowl.
2. Now take any solid object you like and measure its weight using a spring balance. Note this down.
3. Keep the object attached to the spring balance and submerge it in the water. Just make sure the spring balance is not submerged.
4. 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.
5. Collect this water and weigh it. You will find that the weight of the water will be exactly equal to the weight of the object!