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?

Answer

A, C, D

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
or, `(m_(1)+m_(2))=V_(i)rho_(w)g`
`:. V_(i)=(m_(1))/(rho_(w))+(m_(2))/(rho_(w))` ...(i)
Here, `V_(i)=` 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)gtrho_(w)`
therefore, `V_(1)+V_(2)ltV_(1)`
or the level of water will decrease.