Q.State and prove Archimedes principle.

When a body is partially or fully immersed in a fluid, it pushes aside (displaces) some of that fluid, and the displaced fluid pushes back with an UPWARD force on the body, opposing its weight; this upward force is called UPTHRUST or the BUOYANT FORCE, and the phenomenon is BUOYANCY. ARCHIMEDES' PRINCIPLE states this precisely: a body partially or wholly immersed in a fluid experiences an upward thrust EQUAL to the weight of the fluid it displaces, acting through the centre of gravity of the displaced fluid -- symbolically, upthrust = weight of fluid displaced. THE LAW OF FLOATATION follows directly: a body floats in a liquid if the weight of the liquid displaced by its immersed part equals the weight of the body itself. When a body floats, the volume of fluid it displaces equals the volume of the body that is submerged, and the PERCENTAGE of the body's volume submerged equals its relative density with respect to the fluid: for example, an ice cube (density 0.9 g cm$^{-3}$) floating in fresh water (density 1.0 g cm$^{-3}$) has 90% of its volume submerged, but the same cube floating in denser sea water (1.3 g cm$^{-3}$) has only about 69.2% submerged, since less displaced volume of the denser water is needed to support the cube's fixed weight. For an object fully submerged and hanging from a string in a liquid, the string TENSION equals the object's true weight minus the buoyant force: $T=mg-\rho_{\text{liquid}}Vg$, where V is the object's own volume (found from its m …