Question

state and explain Archimedes principle


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Answer 1

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially 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.
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Answer 2

Hi,

Here is your answer,

                                     ARCHIMEDES PRINCIPLE 

The Archimedes principle gives the magnitude of buoyant force on a body. It states that when a body is immersed wholly or partially in a liquid at rest, it experiences an upthrust. The upthrust is equal to the  weight of the liquid displaced by the immersed part of the body and its upthrust acts through the center of gravity of the displaced fluid.

Explanation of Archimedes Principle 

First of all we need to consider a cylindrical body of height h immersed in a fluid. The upward force (F₂) on the bottom of the body is more than the downward force  (F₁) on its top. If p₁ and p₂ are the pressures at upper face and lower face of the body.

The resultant upward force on the body exerted by the fluid is equal to (p₂ - p₁)A.

We know that, p₂ - p₁ = gh

So,             (p₂ - p₁) A = hρgA= mg                          { m = Ahρ }

where, ρ = density of fluid 

              A = cross - sectional area of the body

Thus, the upward force exerted by the fluid on the body is equal to the weight of the displaced fluid.

The following three cases are possible when the body is immersed in the fluid.

→ If the weight of the body is greater than the upward force or upthrust by the fluid acting upward, then the body sinks.

→ If the weight of the body is equal to the upthrust or the weight of the body is just balanced by upthrust, than the body floats partly immersed.

→ If the weight of the body is less than the upward force, then the body floats partly immersed.

 If the total volume of the body Vs and a part Vp of it is submerged in the fluid, than at equilibrium.

     ↔ WEIGHT OF THE BODY = WEIGHT OF FLUID DISPLACED 

                             Vsρsg = Vpρlg

where  s and  l ae the densities of the body and fluid.

                           ρs/ρl = Vp/Vs


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