Archimedes Principle

Archimedes principle deals with the forces applied to an object by fluids surrounding it. This applied force reduces the net weight of the object submerged in a fluid. It is also this physical law of buoyancy that helps us understand how ships float in water.

FormulaDerivationApplicationsExperimentSolved Examples

What is Archimedes Principle?

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”.

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 the liquid displaced by it.

Archimedes Principle Explanation

Archimedes Principle

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 the air) – Thrust force (buoyancy)

Archimedes’s 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 law 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 Experiment

Archimedes Principle Experiment

  • 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!

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 the Archimedes principle, we can write:

The apparent loss of weight = weight of water displaced = ρ×V×g

Thus, the Thrust force is,

\(Thrust\) = \(ρ~×~V~×~g\)

Where,

  • ρ is the density of liquid
  • V is the 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.

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Archimedes Principle Applications

Following are the applications of Archimedes principle:

Submarine:

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

Hot-air balloon:

The reason why hot-air balloons rise and float in mid-air is 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. Hydrometer consists of lead shots which makes them float vertically on the liquid. The lower the hydrometer sinks, the lesser is the density of the liquid.

Archimedes Principle Solved Examples

Q1. Calculate the resulting force, if a steel ball of radius 6 cm is immersed in water.

Ans: Given,

Radius of steel ball = 6 cm = 0.06 m

Volume of steel ball, V = \(\frac{4}{3}\pi r^{3}\)

V = \(\frac{4}{3}\pi 0.06^{3}\)

∴V = 9.05 × 10-4 m3

Density of water, ρ = 1000 kg.m-3

Acceleration due to gravity, g = 9.8 m.s-2

From Archimedes principle formula,

Fb = ρ × g × V

F= (1000 kg.m-3)(9.8 m.s-2)(9.05 × 10-4 m3)

∴Fb = 8.87 N

Q2. Calculate the buoyant force, if a floating body is 95% submerged in water. The density of water is 1000 kg.m-3.

Ans: Given,
Density of water, p = 1000 kg.m-3
From Archimedes principle formula,
Fb = ρ × g × V

or

Vb × ρb × g = ρ × g × V

Where,

ρ,g, and V are the density, acceleration due to gravity, and volume of the water

Vb, ρb, and g are the volume, density, and acceleration due to gravity of body immersed

Rearranging the equation,

\(\rho _{b}=\frac{V\rho }{V_{b}}\)

Since 95% of the body is immersed,

0.95 × V= V

∴ρ= 950 kg.m-3

Frequently Asked Questions – FAQs

What does Archimedes Principle state?

Archimedes’ principle states that an object submerged in a fluid, fully or partially, experiences an upward buoyant force that is equal in magnitude to the force of gravity on the displaced fluid.

Who discovered the Archimedes Principle?

Greek mathematician Archimedes discovered the Archimedes principle.

How does the Archimedes principle apply to ships?

Archimedes continued to do more experiments and came up with a buoyancy principle that a ship will float when the weight of the water it displaces equals the weight of the ship and anything will float if it is shaped to displace its own weight of water before it reaches the point where it will submerge.

Where is the Archimedes principle used?

Archimedes principle is used in the design principle of ships and submarines. Hydrometers are based on the principle of Archimedes.

How can the Archimedes Principle be used to determine the density?

The weight of the fluid displaced is equal to the buoyant force on a submerged object. The mass divided by the volume thus determined gives a measure of the average density of the object.


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5 Comments

  1. MATHEMATICALLY THE CALCULATIONS ARE CORRECT AND AWESOME WOW!!!!!!!! i have found them enjoyable

  2. Thank you sir

  3. What is the meaning of apparent weight here??

    1. When an object is held underwater, it weighs less than it does in the air because the buoyant force is helping to hold it up. Due to this property, the reduced force that you need to apply to hold the object is known as apparent weight.

  4. Geetanshi Singh Rawat

    I am a BYJU’S student and I love BYJU’S and when I was searching for Archimedes law I saw the BYJU’S explanation on the web so I clicked it and I found it really helpful.

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