A piece of ice is floating in a glass vessel filled with water. Then prove that level of water in the vessel remains unchanged after melting of ice.

Explanation

Let `m` be the mass of ice piece floating in water.
in equilibrium, wright of ice `=` uptrust
`mg = V_(i)rho_(w)g`
or `V_(i) = (m)/(rho_(w))`
Here, `V_(1)` is the volume of ice piece immersed in water
When the ice melt, let `V` be the vloume of water formed by `m` mass of ice. Then,
`V_(i) = (m)/(P_(w))`
From Eqs. `(i)` and `(ii)` we see that
`V_(i) = V`
Hence, the level will not change.