Write the law of floatation and describe its cases.

Explanation

When the weight of body is equal to the weight of liquid displaced by the part of the body immerged in it , the body floats on the surface of the liquid.
For example : Boat ,Steamer.
When a body is partially or completely immerged in a liquid , it experiences two froces.
(1) Weight of the body W=mg
`rho_(f)V_(s)f` (in downward)
Where m= volume `xx` density `(V_(s)rho_(s))andV_(s)=` volume of body `,rho_(s)=` density of body.
(2)Buoyant force of body,
`F_(b)`= weight of displaced liquid
`=rho_(f)V_(s)g` (in upward direction)
where `V_(f)`= volume of displaced liquid,
`rho_(f)` = Density of liquid
Cases :
(a) If `WgtF_(b)`, the body sinks.
Example : Piece of iron
(b) If `W=F_(b)` , the body remains in equilibrium at any depth.
Example : Submarine.
(c) If `ltF_(b)` the body floats on the surface of the liquid.
For example : Submarine ,boat
Note : Above relation can be expressed in the form of density of body and density of liquid as below :
(1) `rhogtrho_(0)` body sinks ,where ,`rho=` density of body and `rho_(0)` = density of liquid.
(2) `rho=rho_(0)` body remains in equilibrium at any depth of liquid.
(3) `rholtrho_(0)` , body floats on liquid . At this time volume of part of body appear outside from the surface of liquid.
`V.=V(1-(rho)/(rho_(0)))` , where V= volume pf body