Floatation. When a stone is placed on water, it sinks because its weight is greater than the up thrust. When a cork is held below the surface of water, it rises on release. This is because the up thrust on the cork is greater than its weight.

A piece of wood neither rises nor sinks but floats because the up thrust on the piece of wood and its weigh just balance so it experiences no net force.

In general a body floats because up thrust is equal to weight of the body. A body will sink because up thrust on it is less than the weight of the body.

The principle of flotation states that: A floating body displaces its own weight of fluid i.e. for a floating body; weight of body = weight of displaced fluid 𝑾𝒃=𝑾𝒇

Where Wa is weight of body floating, Wf is weight of displaced fluid.
Where Vf is volume of displaced fluid
Where Vb is volume of floating body, ρb is density of floating body “g” is acceleration due to gravity.

image 139

Example 1:
A piece of cork of volume 100cm3 is floating on water.
If the density of the cork is 0.25gcm-3. Calculate the volume of cork immersed in water.

image 140

Experiment: To verify the Law of Floatation

image 141


A test tube is placed in a measuring cylinder containing water and the original reading of the water level (V1) is noted.

Lead shots are added to the test tube until it floats up right and the new water level (V2) is noted.

Volume of displaced water=(V2−V1)cm3 Weight of displaced water =ρw(V2−V1)𝑔

The test tube together with the shots is removed from the cylinder and weighed using a spring balance. (The cotton loop helps to attach it to the balance hook). Their weight is recorded, 𝐖_.
(Weight of lead shots+testtube)=Wa


The weight of lead shots and test tube is equal to the weight of displaced water.

image 142


From the above observation, it is noticed that the law of floatation is verified.

Application of the law of floatation

image 143

(i) A hydrometer
The relative density of any liquid may be found using a hydrometer.
-It is used to test the purity of milk.
-It is used to test R.D of a car battery acid.
This consists of a float with along stem. A heavy weight is placed beneath the float to keep the hygrometer up right. The higher the hydrometer float the higher the relative density of the liquid.

image 144

(ii) Submarines
The average density of submarines is varied by means of ballast tanks. For the submarines to float, the ballast tanks are filled with air. To sink the submarines, the tanks are filled with water causing average density to rise higher than that of water

(iii) Ships
Why ships float.
Ships float on water, although they are made from iron and steel which are denser than water. This is because a steel or iron ship is made hollow and contains air. So the average density of the ship is less than that of water.

The loading lines called plimsoul marks on the sides show the level to which it can be safely loaded under different conditions.
Weight of displaced water (Ww) = weight of the ship (Ws) + weight of the cargo (Wc).


(iv) Balloons
These are airships used in meteorological measurements.
A balloon filled with hydrogen weighs less than the weight of air it displaces.
The up thrust being greater than its weight, a resultant up ward force on the balloon causes it to rise.
The balloon continues to rise up until the upthrust acting on it is equal to the weight of the balloon plus its content and then it floats.
The lifting power of the balloon is calculated from the formula:

image 145

Example: 1
A balloon has a capacity 10m3and is filled with hydrogen. The balloon’s fabric and the container have a mass of 1.25kg. Calculate the maximum mass the balloon can lift.
{Density of hydrogen = 0.089kgm-3: density of air=1.29kgm-3}


image 146
image 147

Relationship between density of a floating body, density of a liquid and fraction submerged

image 148