Archimede’s Principle

  • When a solid object is immersed in a fluid, an upward force acts on it.
  • The magnitude of the force is given by Archimede’s principle.
  • This principle was propounded by Archimedes (287- 212 BC), a famous Greek scientist.
  • Archimede’s principle states , “ When a body is partially or wholly immersed in a fluid, it experiences an up-thrust which is equal to the weight of the fluid displaced by it.”


Theoretical proof of Archimede’s principle

Let us consider a cylinder of height ‘h’ and uniform cross-section area ‘A’ is immersed in a liquid of density ‘d’.

Image result for archimedes principle derivation

If h1 and h2 are the depths of the upper and lower surfaces of the immersed cylinder,  then

Force on upper face (F1) = P1 × A =h1dgA

Force on lower face (F2) = P2×A =h2dgA [g =acceleration due to gravity]

Now, Up-thrust (U) =F2 –F1

= h2dgA –h1dgA

= (h2 –h1) Adg                                                                    


Let h2 –h1 =h, then,

U =hAdg

= Vdg             [since, V =h×A]

= mg    [ V.d =m]

Therefore, Upthrust(U) = weight of liquid displaced.

Hence, Archimede’s principle is proved.





Archimede’s Principle