**Introduction About Proof of Archimedes Principle:**

**Buoyant force** is the force applied upward on an object by any fluid. **Archimedes’ principle** states that the buoyant force applied to an object is equal to the weight of the fluid the object displaces.watch Introduction About Proof of Archimedes Principle to learn more.

**Proof of Archimedes Principle:**

The fluid is the states of matter. These are classified in two types that are laminar flow and turbulent flow. The first laminar flow includes the predictable flow of fluid particles and follow streamlines. When the flow rate of fluid particles is very large then flows if particles follow with erratic motion. Thus, the region in which the flow lines are constantly changing then it is turbulent flow.

The part of fluid mechanics is **fluid dynamics** which include the study of fluid flow. This is the natural phenomena of movement of fluid. It includes aerodynamics which studies the motion of air and gas and the second is hydrodynamics which includes the study of motion of liquids. So the fluid dynamics is very useful in detecting forces and moments, mass flow rate of petrol in pipelines, detecting knowledge of weather or in traffic engineering.

It is based on some empirical and semi-empirical laws which are derived to solve practical problems and properties of fluid like velocity, density, and pressure temperature. Here we discuss the **principle of Archimedes**. He gave the answer of the question that the reason for floating objects.

**Archimedes Principle Definition:**

The Archimedes Principle States that “When an object floats into the fluid, it displaces the fluid of its own weight.”

Gas is also a kind of fluid.

Hence, the law becomes:

**An object or body, immersed fully or partially in a liquid, experiences a force upwards which is in correspondence with the amount of water or fluid displaced by the object.**We can also say that:

Buoyancy = the weight of the fluid displaced by the object

**Archimedes Principle of Buoyancy**

**Buoyancy is an upward force exerted by a liquid that opposes the weight of immersed object**.

When a body is submerged in a fluid, an upward force is exerted by the fluid on the body. This upward forceis equal to the weight of the fluid displaced by the body and is defined as **force of buoyancy** or simply **buoyancy**. It is very important to note that due to buoyancy the apparent weight of the body being immersed is reduced.

The apparent weight of the object = The original weight – the buoyant force exerted.

**For example:**

- If we have a rock which is hanging on a thread in a pool and initially a force of 20 Newton is exerted by it. Now the force of buoyancy exerted back by water is 3 Newton.

Then the Net force exerted by the rock is 20 – 3 = 17 Newton.

It is noteworthy that it is quite easy to pull an object through water than to actually lift it from the bottom of a water pool.

- The hot air balloon rises in the air as the density of the warmer air inside the balloon is less than the cooler air outside the balloon. There is a buoyant force acting on the system and so the balloon as well as the basket displaces a fluid that is heavier than both of them. This is the reason balloons tend to fly better in the morning as the surrounding air is cool.

This rule is very useful in determining the density and volume of an irregular object. It is done by measuring its mass in the air and also when it is submerged in water.

The force of buoyancy would be the same for the equal masses of the objects, as it does not depend upon the type of the matter, the object is made of.

**Archimedes Principle Equation**

Buoyant force is given by:

**F _{b} = g **ρ

**V**.

**…………………..(1)**Also

**F**

_{b}= W_{a}– W_{f}**……………….(2)**where,

F = Buoyant force

g = Acceleration due to gravity

ρ = Density of the fluid

V = Volume of the object inserted into the fluid

**F**is the Buoyant force

_{b}**W**= the Normal weight of the object when it is in air

_{a}**W**= the Apparent weight of the object when it is immersed in the fluid

_{f}Hence using (1) in (2)

**g **ρ** V = W _{a} – W_{f }……………………………..(3)**∴

**V**= Wa–Wfgρ ……………….(3)and putting it in the formula for density we get:

ρ = Wa–Wfgv ………………………(4).

Useful for CBSE, ICSE, NCERT & International Students

Grade :9

Subject : Physics

Lesson : Gravitation

Topic:Proof of Archimedes Principle

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