1. FLOATATION AND RELATIVE DENSITY – GRADE 9
Weight W is the force acting vertically downwards, through the centre of gravity G. W has a tendency to sink the body.
While Upthrust FB of liquid acting vertically upwards, through the centre of bouyancy B i.e. the centre of gravity of the displaced liquid.
Note : B coincides with G for a body with uniform composition, if the body is completely submerged.
B lies vertically below the centre of gravity, if the body is floating with its part submerged.

2. W = volume of the body X density of the body X g FB = volume of submerged part of the body X density of liquid X g

3. W-FB will be the apparent weight acting vertically downwards
Case 1 W > FB (this is the case when the density of solid > density of the liquid.
The body will sink
W-FB will be the apparent weight acting vertically downwards

4. Case 2 W = FB (this is the case when the density of body = density of the liquid.
The body will just float below the surface of the liquid
Apparent weight of the body will be zero.

5. W= FB only due to the submerged part of the body.
Case 3 W < FB (this is the case when the density of body < density of the liquid.
The body will float partially above and partially below the surface of the liquid
Only that much portion gets submerged by which the weight of displaced liquid becomes equal to the weight of the body.
W acts at the centre of gravity of the body, while FB acts at the centre of buoyancy B which is vertically below G
W= FB only due to the submerged part of the body.

7. PRINCIPLE OF FLOATATION
The weight of a floating body is equal to the weight of the liquid displaced by its submerged part. Thus the weight of the body is balanced by upthrust (weight of the liquid displaced by its submerged part) on it .

8. APPARENT WEIGHT = TRUE WEIGHT – UPTHRUST
= 0
Thus a floating body appears to have no weight (or its apparent weight is zero)
W = V ρs g
FB = v ρL g
For floatation W = FB
V ρs g = v ρL g

9. APPLICATIONS OF THE PRINCIPLE OF FLOATATION
Floatation of iron ship
An iron nail sinks in water while a ship floats
A loaded ship is more submerged while an unloaded ship is less submerged
A ship begins to submerge more as it sails from sea water to river water
Plimsoll line indicates the safe limit for loading the ship in water
An unloaded ship is filled with sand at its bottom

11. Floatation of human body –
It is easier for a man to swim in sea water than in fresh water e.g. a man can easily swim in dead sea with very small portion of his body inside water and shoulders all the time above water.

12. Floatation of Submarines –
Submarine is a fish shaped water-tight boat provided with several ballast tanks.
It can be made to dive into water or rise up to the surface of water as and when desired.

13. Floatation of ice-berg
The density of ice (0.917 g/ 𝑐𝑚 3 < density of water 1 g/ 𝑐𝑚 3 )
𝑣 𝑉 = ρice ρwater

14. Floatation of fish
When the fish has to rise up in water, it diffuses gas from its fluid into the bladder so its volume increases and its average density decreases.
When it has to come down, it empties its bladder to the required extent so its volume decreases and density increases

15. Rising of balloons
Lighter gases like hydrogen or helium is filled in a balloon.
The weight of he air displaced by he inflated balloon (upthrust) becomes more than the weight of the gas filled balloon and it rises up.
The balloon does not rise indefinitely.