Question

Why there is no change in water level on melting a floating piece of ice

Answer 1

If the material in the water is denser than the water, it will sink and it will displace a volume of water equal to the object's own volume.

If the material in the water is less dense than the water, then it will float. It will displace a certain amount of water, but less than the volume of the object since only part will be submerged and the rest will be floating above the surface. So, how much water is displaced? Well, the mass of the water displaced will be equal to the mass of the object for anything that floats. For extremely light objects, like styrofoam, hardly any water is displaced and the material floats high in the water.
Ice, which is only slightly less dense than water and which is much denser than styrofoam displaces a larger amount of mass and thus floats much lower in the water.


So, the mass of water displaced is equal to the mass of the object floating in it. The volume of the water displaced by the object is equal to the mass of the object or the mass of the displaced water (since they are the same) divided by the density of water. When the ice melts, it becomes denser and adopts the same (neglecting temperature effects) density as the water it has been resting in. Since there is no change in mass, the melt water perfectly fills in the region of displaced water and there is no change in the water's level.

For example, 4kg of ice displaces 4kg of water it is floating in. When the ice melts, it becomes 4kg of water, exactly equal to the 4kg previously displaced and at the same density, so the water level does not change.