- 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’.
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,
= Vdg [since, V =h×A]
= mg [ V.d =m]
Therefore, Upthrust(U) = weight of liquid displaced.
Hence, Archimede’s principle is proved.