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.

Explanation

Let `M=` Mass of the floating solid
`rho_(2)`=density of liquid formed by the melting of the solid
`rho_(1)`=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)/(rho_(1))`.
When the solid melts, the volumes occupied by it is `(M)/(rho_(2))`. Hence the level in container will rise or fall according as
`(M)/(rho_(2)) gt` or `lt(M)/(rho_(1))` i.e. `rho_(2)lt `or` gtrho_(1)`
There will be no change in the level if `rho_(1)-rho_(2)`. In case of ice, floating in water `rho_(1)=rho_(2)` and hence, the level of water remains unchanged when ice melts.