Question

define law of floatation and discuss the case arises

Answer 1

The Law of Flotation says that for a floating object, the weight of the object equals the weight of the liquid displaced by the object. We prove this by using Archimedes' Principle with Newton's Second law applied to an object in equilibrium (floating).
The case that is relevant to the question is as follows:
[Note: The 'downward' direction is the direction of earth's gravity.]
When an object is immersed in a fluid, its weight (force caused by the gravity) will tend to pull it downwards. 

A fluid tends to exert pressure (due to the constant motion of its particles).

When an object is immersed, its base will be acted upon by the upward pressure of fluid. If the object is completely immersed, its upper half will also experience a pressure in the downward direction. The pressure pushing the object downwards will be lesser than the pressure upwards because of the difference in depth. (As the depth increases, the pressure increases.) 

Answer 2

Archimedes’ principle, physical law of buoyancy, discovered by the ancient Greek mathematician and inventor Archimedes, stating that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface for an object partially submerged in a liquid. The weight of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. The buoyant force on a body floating in a liquid or gas is also equivalent in magnitude to the weight of the floating object and is opposite in direction; the object neither rises nor sinks. For example, a ship that is launched sinks into the ocean until the weight of the water it displaces is just equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo.
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