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How do you appreciate Archimedes discovery of the force of buoyancy?

Answer
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Hint:The object would be submerged, or it will float, this all will depend upon the balance of forces, i.e. force due to the weight of the body and the force of the buoyant action. Also, the line of application of both the forces must be the same, and the forces must be equal and opposite.

Complete step by step answer:
The whole concept lies in the force interaction, one because of the weight and one coming from beneath the liquid in a vertical direction. If these two forces become equal, then the component is in a floating condition.
 In case of a ship, the force of thrust due to the small drowned section of the ship is equal to the weight of the whole ship body that is why the ship floats.
 We can also correlate that why an oil pin sinks. It is because, as the density of steel is more than that of water. So the force due to the weight of the pin is more than that of the force due to the buoyant action. Therefore, the pin is drowned.
 Therefore, the Archimedes discovery of the force of buoyancy makes it possible to analyse the stability of the floating and submerged objects.

Note:Since air is also a fluid and a balloon filled with hydrogen gas floats in air space since the buoyant force calculated by the weight of the displaced volume of air by the balloon is equal to the low value of the hydrogen gas acting downwards. Since the buoyant force calculated by the weight of the volume displaced by the balloon is equal to the low weight of the hydrogen gas acting downwards.