Why does a ship made of iron float while a piece of iron of same mass sink in water?

It’s because an iron ship is not completely solid. It has full of air filled in it. So the average density of the ship as a whole is less than the density of water. Therefore immersed portion of the ship displaces water equal to its weight. So the ship floats whereas a sheet of iron is compact and there are no air spaces inside it. Iron is denser than that of water. The weight of the sheet is greater than the weight of the water displaced by the sheet. So it sinks.

Since the ship is designed in such a way that its effective density (m/V) is less than the density of the water.

V = volume of ship

m =mass of ship.

So it floats upon the water. Hence the ship does not sink.

For the nail,

The density of nail (as of iron) is much larger than the water. So it sinks easily.

Also

Archimedes' principle states that

Weight of liquid displaced = Buoyant force

The weight of the water displaced by the ship is equal to its weight, so it floats. Whereas the weight of the water displaced by the iron nail is less than its weight so the iron nail sinks.

Example

Consider an iron bar of 20 Kg with 10cm length, 10cm width and 10cm height.

Volume of the bar = 10 x 10 x10 = 1000 cm³

Weight = 20 Kg = 20000 gram

Density of the iron bar  = Weight / Volume = 20,000/( 10x10x10) = 20 gram/cm³

The same iron bar is constructed as a ship with air volume 25,000 cm³

Now the total volume of the ship = Volume of the iron bar + Volume of the air space in the ship = 25,000+(10x10x10)  

Density of the ship with the same iron bar = Weight / Volume

                                                                     = 20,000 / {25,000+(10x10x10) }= 0.7692 gram/cm³

So, Density decreases when there is more air space. So the average density of the ship as a whole is less than the density of water. Therefore immersed portion of the ship displaces water equal to its weight.