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## Monday, December 4, 2017

### Archimedes' Principle

•    The Archimedes' Principle is named after Archimedes of Syracuse
•    He discovered the law in 212 B.C.
•    The Archimedes' Principle states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Mathematically, the Archimedes' principle can be stated as Buoyancy = weight of displaced fluid.

Buoyant Force- When a body is immersed partially or completely in a liquid, a force acts in the upward direction by the liquid surface on the body. This force is called Buoyant Force, also sometimes referred as upthrust or force of buoyancy. The force is equal to the weight of the liquid displaced by the body and acts at the center of gravity of displaced liquid. This naturally occurring phenomenon makes the basis for Archimedes’ Principle as stated above.

### Law of Floatation

A body floats in a liquid if-

•    Density of material used in the body is less than or equal to the density of liquid in which it is immersed.
•    If Density of material of body is equal to density of liquid, the body floats fully submerged in liquid in neutral equilibrium.
•    When a body floats in neutral equilibrium, the weight of the body is equal to the weight of liquid displaced.
•    The center of gravity of the body and center of gravity of the displaced liquid should be in one vertical line.

Centre of Buoyancy – The center of gravity of the liquid displaced by a body is called center of buoyancy.

Meta Center- When a floating is slightly tilted from equilibrium position, the centre of buoyancy shifts. The point at which the vertical line passing through the new position of center of buoyancy meets with the initial line is called meta centre.

### Conditions for Stable Equilibrium of Floating Body

•    The meta centre must always be higher than the gravity centre of the body.
•    The line joining the centre of gravity of the body and centre of floatation should be vertical.

Density – Density is defined as mass per unit volume.
Mathematically, Density = Mass / Volume.
The SI unit of density is Kg/m3

Relative Density = Density of Material / Density of Water at 40C
• The relative density is ratio and hence unitless.
• The relative density is measured by instrument called Hydrometer.
• The density of sea water is more than that of normal water. This is why it is easier to swim in sea water.
• If ice floating in water in a pot melts, the level of water in the vessel does not change.
• When ice floats in water, its 1/10th part stays remain outside of water surface.
• Purity of Milk is measured by an instrument called lactometer.