Archimedes’ Principle Formula

When the object is immersed in the fluid, the object feels lighter due to the loss of apparent weight which is equal to the weight of the fluid displaced by the liquid.

FB = ρ × VL × g

Where,

  • FB is the Upward Thurst or the Buoyant Force
  • ρ is the Density of the Fluid
  • VL is the Volume of the Fluid Displaced
  • g is the Acceleration Due to Gravity

Archimedes Formula Derivation

Lets take a cylinder ‘PQRS’ with upper surface ‘PQ’ and lower surface ‘RS’, dipped in a liquid of density DL the height of the cylinder is ‘h’ and it is at a depth ‘d’. Since the depth at PQ is d and at RS is (d+h)

Using the formula for pressure (P = ρ × h × g)

PPQ = DL × d × g

PRS = DL × (d+h) × g

According to the laws of liquid pressure, pressure at a point inside the liquid increases with the depth from its free surface.

So, PPQ < PRS

According to the laws of liquid pressure, liquid pressure is the same in all directions about a point in a liquid. So, there will be an upward force acting on the bottom surface RS, which is the Upthrust or Buoyant Force

FB = P × A where P is Pressure and A is Area

FB = (PRS – PPQ) × A

FB = ((DL × (d+h) × g) – (DL × d × g)) × A

FB = DL × g × ( d + h – d) × A

FB = DL × g × Ah

FB = DL × g × Vo …………….. Volumeobject = volume of cylinder = Area × height

FB = DL × VL × g …………….. Volumeobject = Volume liquid displaced

Archimedes Principle Cases

There are three possible cases as per Archimedes Principle, these cases are mentioned below:

Case 1: If the FB = Weightobject then the object will float in completely submerged position;

Case 2: If FB > W then the object will float;

Case 3: When FB < W then the object will sink.

Archimedes Principle and Buoyancy

Archimedes Principle in simple words states that when an object is immersed in water it displaces the amount of liquid weight of the object. When object is immersed it experiences an upward force called buoyant force. The magnitude of this buoyant force is equal to the weight of the object immersed.

Archimedes Principle

Archimedes Principle is a fundamental concept in fluid mechanics, credited to the ancient Greek mathematician and physicist Archimedes. According to Archimedes’ Principle, when an object is immersed in a fluid the object experiences an upward force whose magnitude is equal to the weight of the fluid displaced by the object.

Archimedes’ principle has applications in various fields, from ship design to understanding the behavior of objects in water. Archimedes’ Principle is important for class 9 students.

In this article, we are going to learn about what is Archimedes Principle, its formula, how to derive it, its application, and its experimental verification of Archimedes

Table of Content

  • What is Archimedes’ Principle?
  • Experimental Verification of Archimedes’ Principle
  • Archimedes’ Principle Formula
  • Applications of Archimedes’ Principle
  • Solved Examples

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What is Archimedes’ Principle?

Archimedes Principle states that when an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle explains why objects appear to weigh less when placed in a fluid and why some objects float while others sink. The buoyant force is directly proportional to the volume of the fluid displaced by the submerged object, and it counteracts the object’s weight. As a result, if the weight of the fluid displaced is greater than or equal to the weight of the object, it will float, while if the weight of the fluid displaced is less, the object will sink....

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Archimedes’ Principle Formula

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Applications of Archimedes’ Principle

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Solved Examples of Archimedes’ Principle

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Practice Problems on Archimedes’ Principle

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