# 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, i**t 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 **h _{1}** and

**h**are the depths of t

_{2}**he upper and lower surfaces**of the immersed cylinder, then

Force on upper face **(F _{1})** = P

_{1 }× A =h1dgA

Force on lower face **(F _{2})** = P

_{2}×A =h

_{2}dgA [g =acceleration due to gravity]

Now, Up-thrust **(U) =F _{2} –F_{1}**

= h_{2}dgA –h_{1}dgA

= (h_{2 }–h_{1}) Adg* *

Let h_{2} –h_{1} =**h**, then,

U =**h**Adg

= Vdg [since, V =**h**×A]

= mg [ V.d =m]

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

Hence, Archimede’s principle is proved.

**References:**

i) https://www.sciencedirect.com/topics/engineering/archimedes-principle

ii) https://www.livescience.com/58839-archimedes-principle.html

iii) https://physics.weber.edu/carroll/archimedes/principle.htm