How is the density of the body directly proportional to buoyant force?

Archemedes principle states that when a body is immersed wholly or partially in a liquid, it experiences an upward buoyant force of magnitude equal to the weight of the liquid displaced by it.

Buoyant force = Weight of displaced liquid

Weight of displaced liquid = Mass of the displaced liquid × Acceleration due to gravity

= Density of the liquid × Volume of the displaced liquid × Acceleration due to gravity

∴Volume of the displaced liquid = Volume of the object that is immersed in the liquid

∴Weight of the displaced liquid = Volume of the object immersed in the liquid × Density of the liquid × Acceleration due to gravity

Therefore we can write,Buoyant force = Volume of the object × Density of the liquid × Acceleration due to gravity

As the above equation for buoyant force suggests, the magnitude of the buoyant force is directly proportional to the density of the fluid. A body with greater density will exert a greater force on the water.