Archimedes’ Principle   states that when a body is completely  or partially  immersed in a fluid, it experiences an upthrust or loss in weight which is equal to the weight of the fluid displaced by the body.

From this principle, the following can be deduced.

1. Upthrust = loss in weight=W-T
2. Upthrust= weight of the fluid displaced.

From 1.  When a body is held in the air with a rope, the tension T in the rope is equal to the weight of the body. T = W .

When this body is released into a liquid, there is upward force called upthrust U which push the body upward. Then U + T=W . therefore U=W-T.  See fig above.

From 2  above

When the body is fully immersed, there is an increase in total level of the liquid which  can be converted to volume and weight.

Upthrust = loss in weight = weight in air – weight in water

= change in volume x density of the liquid

But change in volume = volume of object immersed

Upthrust = volume of the object x density of the liquid

From fig 1 above

Initial volume before object =v1

Final volume after object is immersed= v2

Change in volume = v2-v1= volume of the object immersed.

If the object is a cube then volume is=LX L X L=  

The volume of the liquid displaced by the object  =

Therefore

But upthrust =

When a body is partially immersed

For example       of the volume of the body is immersed

Upthrust =   V of the object x density of liquid

Verification  of Archimede's Principle

 An object is attached to a spring balance and its weight noted as w1

The object is is immersed in a liquid of density D and its weight noted as w2

The volume and weight of the displaced liquid was measured as v

 it was found that the loss in weight w1-w2 is equal to the weight of the liquid displaced.

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