Advanced Physics Topics like quantum mechanics and relativity have revolutionized our understanding of the universe.

## Archimede’s Principle: Definition and Application

When a solid object is immersed (or dipped) in a liquid, an upward ‘buoyant force’ acts on the object. The magnitude of this buoyant force is given by Archimedes’ principle.

According to Archimedes’ principle : When an object is wholly (or partially) immersed in a liquid, it experiences a buoyant force (or upthrust) which is equal to the weight of liquid displaced by the object. In other words :

Buoyant force (or Upthrust) acting on an object = Weight of liquid displaced by that object

For example, if a stone, on being immersed in water, displaces ’10 newtons’ weight of water, then according to Archimedes’ principle, the buoyant force acting on this stone will be equal to ’10 newtons’. Thus, the magnitude of buoyant force acting on an object immersed in a liquid is equal to the weight of liquid displaced by the immersed object.

Please note that even gases (like air) exert an upward force (or buoyant force) on the objects placed in them but in most cases it is so small that we usually ignore it. In fact, Archimedes’ principle is applicable to objects in liquids as well as gases. Now, liquids and gases are known by the common name of ‘fluids’. So, sometimes the word ‘liquid’ in the definition of Archimedes’ principle is replaced by ‘fluid’ to make it more general. Thus, Archimedes’ principle can also be stated as : When an object is wholly (or partially) immersed in a fluid, it experiences . a buoyant force (or upthrust) which is equal to the weight of fluid displaced by the object. It is the buoyant force (or upthrust) due to displaced air which makes a balloon rise in air. We will now solve a numerical problem based on Archimedes’ principle.

**Example Problem.**

When an aluminium object is immersed in water, it displaces 5 kg of water. How much is the buoyant force acting on the aluminium object in newtons ? (g = 10 m/s^{2}).

**Solution.**

According to Archimedes’ principle, the buoyant force acting on this aluminium object will be equal to the weight of water displaced by this aluminium object. So, all that we have to do is to find the weight of water displaced in ‘newtons’. That will give us the buoyant force. We know that :

Weight, W = m × g

Here, Mass of water, m = 5 kg

And, Acceleration due to gravity, g = 10 m/s^{2}

Now, putting these values of m and g in the above formula, we get :

Weight of water, W = 5 × 10 N = 50 N

Now, since the weight of water displaced by the aluminium object is 50 newtons, therefore, the buoyant force acting on the aluminium object (due to water) will also be 50 newtons.

### Applications of Archimedes’ Principle

Archimedes’ principle has many applications (or uses). The important applications of Archimedes’ principle are given below :

- Archimedes’ principle is used in determining the relative density of a substance.
- The hydrometers used for determining the density of liquids are based on Archimedes’ principle.
- The lactometers used for determining the purity of milk are based on Archimedes’ principle.
- Archimedes’ principle is used in designing ships and submarines.

We will describe all these applications of Archimedes’ principle in detail in higher classes. At the moment, we will explain why some objects float whereas others sink in a liquid.