A piece of ice having a stone frozen in it floats in a glass vessel filled with water. How will the level of water in the vessel change when the ice melts?

Explanation

Let, `m_(1)`=mass of ice, `m_(2)`=mass of stone,
`rho_(s)`=density of stone , and `rho_(w)`=density of water.
In equilibrium, when the piece of ice floats in water,
weight of (ice+stone)=upthrust
`(m_(1)+m_(2))g=V_(i)rho_(w)g`
`therefore " " V_(i)=(m_(1))/(rho_(w))+(m_(2))/(rho_(w))`
Here, `V_(1)`=Volume of ice immersed
When the ice melts, `m_(1)` mass of ice converts into water and stone of mass `m_(2)` is completely submerged.
Volume of water formed by `m_(1)` mass of ice, `V_(1)=(m_(1))/(rho_(w))`
Volume of stone (which is also equal to the volume of water displaced )
`V_(2)=(m_(2))/(rho_(s))` Since, `rho_(s) gt rho_(w)`
Therefore, `V_(1)+V_(2) lt V_(i)`
or, the level of water will decrease.