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 equilibriumm, When the piece of ice floats in it floats in a water, weight of `("ice"+"stone") = "upthrust"`
`(m_(1) + m_(2))g = V_(1)rho_(w)g`
`:. V_(1) = (m_(1))/(rho_(w)) + (m_(2))/(rho_(w))`
Here, `V_(i) =` Volume of ice immersed
when the ice melts `m_(1)` mass of 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 isplaced)
`V_(2) = (m_(2))/(rho_(s))`
Since, `rho_(s) gt rho_(s)`
Therefore, `V_(1) + V_(2) lt V_(1)`
or, the level of water will decrease.