A piece of ice with a stone in it is floating on water in a beaker. Will the level of water in the beaker change after complete melting of the ice?

Explanation

If ice melts completely, the level of water in the beaker goes down.
Let the density of water be `rho`, the weight of ice be W and the weight of stone be w.
`therefore" "`Weight of displaced water
= weight of ice + weight of stone = (W + w)
`therefore" "` Volume of displaced water = `V_(1)=(W+w)/(rhog)`
Let the density of the stone be `rho_(s)`.
Suppose the ice melts completely. In this case, mass of water thus formed due to melting of ice = W and volume of this water = `W/(rhog)`. In this situation, the piece of stone will sink into water. Volume of water displaced by the stone = `w/(rho_(s)g)`.
`therefore" "` Total volume of water formed due to melting of ice and also due to displacement by stone
`=V_(2)=W/(rhog)+w/(rho_(s)g)`
`because" "rho_(s)gt1" "therefore" "V_(2)ltV_(1)`
So, when all the ice melts, the level of water in the beaker goes down.