Law of floatation:-

Law of flotation

Law of floatation states that weight of a floating body is equal to the weight of liquid displaced by it.

Mathematically, 
Weight of a floating body, W_{floating body} = Weight of liquid displaced, W_{liq displaced}.

Condition for floatation of a body:-

Weight of a floating body, W_{floating body} = Weight of liquid displaced, W_{liq displaced}.

Condition for sinking of a body:-

Weight of a floating body,W_{floating body} > Weight of liquid displaced, W_{liq displaced}.

Law of floatation is a special condition of Archimedes' principle.

Archimedes' principle states that upthrust experienced by a body immersed fully or partially in a fluid is equal to the weight of fluid displaced by the body.

Mathematically,

Upthrust,U = Weight of displaced fluid, Wₒ

In figure A :-

Upthrust(U) exerted by the liquid is less than W₁. W₁ acts vertically downward(↓) and U acts vertically upward(↑). As U < W₁ so net force is vertically downward(↓) and body sinks.

From Archimedes' principle, Upthrust = Weight of liquid displaced(Wₒ).

Condition for a body to sink:-  Wₒ < W₁.

In figure B :-

Upthrust(U) exerted by the liquid is equal to W₂.  W₂ acts vertically downward(↓) and U acts vertically upward(↑). As U = W₂ so net force is zero and body floats in liquid.

From Archimedes' principle, Upthrust = Weight of liquid displaced(Wₒ).

Condition for a body to float :-  Wₒ = W₂.

Instruments based on law of floatation

• Hydrometer like lactometer, alcoholometer, saccharometer, battery hydrometer, etc.
• Boats and ships.
• Flush tank of toilet.
• Automatic liquid volume indicator.