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, M be the mass of stome and ice piece respectively. As ice piece with stone of mass `(m+M)` floats in water, so mass of water displaced in `(m+M)` . If `rho_(w)` is the density of water, then volume of water displaced is
`V=(M+m)/(rho_(w))`..(i)
When the ice melts completely, there will be extra water of mass M and volume `M//rho_(w)` in the beaker. Now the stone will sink and will displaced water equal to its volume `(=m//rho_(s))` , where `rho_(s)` is the density of stone. Thus the total volume of extra water obtained by melting of ice and displaed by sinking stone is
` V' = (M)/(rho_w) +(m)/(rho_s)` ..(ii)
As ` rho_(s) gt rho_(w)`, so ` 1/(rho_s) lt 1/(rho_w) and (m)/(rho_s) lt m/(rho_w)`
From (i) and (ii) we note that :
`V' gt V` . it means the level of water in the beaker will come down.