Archimedes’ principle and its statement and applications

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Archimedes’ principle states that when a body is immersed partially or completely in a liquid, it experiences an upthrust, which is equal to the weight of the liquid displaced by it. This principle of Archimedes applies equally well to gases also. So the principle can be stated alternately as follows:

Archimedes’ Principle states that when a body is wholly or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced.

Application of Archimedes’ principle

Archimedes’ principle and law of floatation can explain several phenomena.

  • An iron nail sinks in water whereas a ship made of iron and steel floats.
  • A ship sinks less in seawater compared to river water. It is for this reason that a ship rises a little when it enters the sea from a river.
  • It is because of the higher density of seawater that it is easier to swim in the sea.
  • When large ballast tanks of a submarine are filled with water the average density of the submarine becomes more than that of water and it can dive easily. When the submarine is ready to surface, ballast tanks are emptied with compressed air, thus reducing the density of the submarine which can then rise.
  • A solid chunk of iron will sink in the water but float in mercury because the density of iron is more than that of water but less than that of mercury.
  • A balloon filled with light gas, such as hydrogen, rises because the average density of the balloon and the gas is less than that of air.
  • Ice, being less dense than water, floats in it with one-tenth of its volume above the surface.

What is the expression of upthrust?

Upthrust = F = weight of the liquid displaced = Vρg where V = volume of the liquid displaced, ρ is the density of the liquid displaced, and g is the acceleration due to gravity.
(Note that, Vρ is the mass and Vρg is the weight of the liquid displaced)

What is the expression of apparent weight?

Apparent weight = Actual weight of the body in air – Upthrust

What is the apparent weight of the body which is floating? (during floatation)

During floatation, upthrust = actual weight of the body …(1)
As we know, Apparent weight = Actual weight of the body in the air – Upthrust …(2)
hence, from 1 and 2 in this floatation case, the apparent weight of the floating body = 0

Related study: Upthrust

Archimedes’ principle and its statement and applications
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