- The value of thrust force is given by Archimedes principle.
- It was discovered by Archimedes of Syracuse of Greece.
- Archimedes’ principle states that when a body is immersed fully or partially in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it.
- Thus, Buoyant force (or Upthrust) acting on an object = Weight of liquid displaced by that object.
- 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.
- Even gases (like air) exert an upward force (or buoyant force) on the objects placed in them.
- It is the buoyant force (or upthrust) due to displaced air which makes a balloon rise in air.

__Apparent weight:__

- Consider a body submerged in water as shown in figure.
- The weight of the body 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.
- Since 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:

__Archimedes principle equation/ Law of buoyancy:__

The mass of the liquid displaced is

$\mathrm{Mass}=\mathrm{Density}\times \mathrm{Volume}=\mathrm{\rho}\times \mathrm{V}\phantom{\rule{0ex}{0ex}}[\mathrm{since},\mathrm{\rho}=\mathrm{Mass}/\mathrm{Volume}=\mathrm{M}/\mathrm{V}]$Thus the weight of that displaced liquid is:

Weight = Mass x Acceleration due to fravity

$\mathrm{W}=\mathrm{M}\times \mathrm{g}=\mathrm{\rho}\times \mathrm{V}\times \mathrm{g}$Thus from Archimedes principle, we can write:

Apparent loss of weight = weight of water displaced =

$\mathrm{\rho}\times \mathrm{V}\times \mathrm{g}$

Thus the Thrust force is,

$\mathrm{Thrust}=\mathrm{\rho}\times \mathrm{V}\times \mathrm{g}$Where,

$\mathrm{\rho}=\mathrm{density}\mathrm{of}\mathrm{liquid}\phantom{\rule{0ex}{0ex}}\mathrm{V}=\mathrm{volume}\mathrm{of}\mathrm{liquid}\mathrm{displaced}$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.

__Experiment to Prove Archimedes Principle:__

- Take a mug filled with water to the brim and place it in an empty bowl.
- Now take any solid object and note its weight by measuring using a spring balance.
- Keep the object attached to the spring balance and submerge the object in the water making sure the spring balance is not submerged.
- Now, note down the weight shown by the spring balance.
- You will notice that it is less.
- Collect the water displaced into the bowl and weigh it.
- You will find that the weight of water will be exactly equal to the loss of weight of the object. This proves Archimedes’ principle.

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