Question

A solid floats in a liquid of different material. Carry out an analysis to see whether the level of liquid in the container will rise or fall when the solid melts.

Answer 1

Let M = Mass of the floating solid 

ρ₁ = density of liquid formed by the melting of the solid

ρ₂ = density of the liquid in which the solid is floating

The mass of liquid displaced by the solid is M. Hence, the volume of liquid displaced is M/ρ₁.

When the solid melts, the volume occupied by it is M/ρ₁. Hence, the level of liquid in container will rise or fall according as

There will be no change in the level if  ρ₁ = ρ₂ . In case of ice floating in water ρ₁ = ρ₂ and hence, the level of water remains unchanged when ice melts.