Since childhood we all know that Because of density low density objects float on high density fluids. But its really interesting to know about the reason why density is responsible. So lets go deep,

If you are not a science student in college or if you are a school student I need to introduce you to some important basic concepts in world of Fluids.

Buoyancy / Buoyant Foce : When any body, is immersed in any fluid, opposite to the weight of that body fluid also applies an upword force which will resist that body to come down. Even Air as a fluid applies buoyancy (we call it air resistance.) Denoted by symbol 'Fb'. Buoyant force is equal to the weight of fluid displaced by object according to Archimedes theorem.

Density : Quantity of mass contained in body per unit volume. denoted by 'd' 

Gravitational Acceleration : denoted by 'g'. value of g is 9.81 meter per sq second.

Archimedes Principle : Archimedes principle states that any body if immersed in a fluid, that body displaces that fluid equal to self volume. volume denoted by 'Vo'. 

Buoyant Force and Weight force of the body oppose each other so resultant decides whether body will float or get immersed.

Logic :


Consider an Object having volume 'Vo', when it will get immersed in water, according to archimedes it will displace water having volume equal to that of the object 'Vo'. 

So the mass of that displaced water will be 'dw',
So weight of that displaced liquid will be equal to dw g Vo.

Hence Buoyant Force will be equal to dw g Vo. 

Weight of the object is W = mg, 
If density of object is do then  mass of that object will be do Vo
Hence weight of object will be W = do Vo g.

If Buoyant Force will be Greater Body will float on surface of water. If  Weight force will be greater Body will sink and go to Bottom.

Case I : Body will immerse in water

In this case Weight force will be more than Buoyant force,
 So 

W > Fb
doVog > dwVog 

Vo and g are common hence get cancelled. 
so 

do > dw
ie Density of object is higher than water,

 
Case II : Body will float on surface of water.

with the same mathematical way,

do < dw
Density of object is less than water.


Case III : Both the densities are same.

In such case whenever we apply force on the body, that force is considered to be virtually acted as a point force, Just like Centre of Gravity, Centre of pressure, 

Simillarly, in buoyancy the virtual point where the total buyant force is supposed to be acted is called Centre of Buoyancy, and that point is at the level which is Half of the depth of water/Fluid.

So if any body having equal density will try to sink then it wont be able to go upto the bottom it will float in half height of the level.


So here we Mathematically proove the Practical Condition on What will be the behaviour of body after immersed in Fluid.