Ship made of iron doesn't sinks but iron nail sinks. Why?
Archimedes says:
Force up on ship or nail - weight of water displaced which is density of water times g times VOLUME OF WATER DISPLACED.
In the case of the ship, assuming it is not full of water, the volume of water displaced includes the volume of the inside of the hull which may be mostly air. Therefore the force up is far greater than it would be if the ship were solid iron.
By the way, if the ship had a hole in the bottom, so that it filled with water, it would sink just like the nail.
The reason why a ship made of iron floats while an iron nail sinks is due to a concept called buoyancy. Buoyancy is the upward force exerted by a fluid (in this case, water) that opposes the weight of an immersed object.
When a ship is designed and constructed, it is carefully engineered to displace a large amount of water—more than its own weight. This displacement creates the upward buoyant force that allows the ship to float. The shape of the ship's hull is designed in such a way that the weight of the ship is evenly distributed over a large volume, which helps maximize the displacement of water and thus the buoyant force.
On the other hand, a small iron nail is much denser and has significantly less volume than a ship. When an iron nail is placed in water, the weight of the nail is greater than the buoyant force exerted on it by the water. As a result, the nail sinks. Density plays a crucial role here—the density of the iron nail is much higher than the density of water, leading to sinking.
So, to summarize, the ship floats because it is designed to displace a large volume of water, generating enough buoyant force to counteract its weight. The iron nail sinks because its weight is greater than the buoyant force it experiences due to its higher density compared to water.