Question

Why does a nail sink into the water but a piece of cork float on water

Answer 1

A nail sink into the water because it has very high density compared to piece of cork.Thus the upthrust on cork is greater than its weight,but is not so nail.

Answer 2

The density of the nail (≈ 7.8 gcm-2) is more than the density of water (≈1 gcm-2), therefore the weight of the nail is more than the upthrust experienced by it causing it to sink.  

However, A boat floats because the boat is hollow from inside and this space is filled with air which reduces the average density of the boat lower than that of water.  

Thus even with a small portion of the boat submerged underwater, the weight of the water displaced by it becomes equal to the weight of the entire boat attaining a floating equilibrium.

According to the Principle of Floatation  

If the weight of the object is greater than the upthrust, then the object will sink in the fluid.

If the weight of the object is equal to the upthrust, then the object is balanced making the object float.

(Upthrust is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object)

Hence, A Boat floats in water whereas An Iron Nail sinks in water