A boat floating in a water tank is carrying a number of large stones. If the stones are unloaded into water, what will happen to the water level?

Explanation

Suppose W and w be the weights of the boat and stones respectively. First, we consider that the boat is floating. It will displaced `(W + w) × 1 cm^(3)` of water. Thus displaced water = (W + w) `cm^(3)` [As density of water `= 1 gm//cm^(3)`]
Secondly, we consider that the stones are unloaded into water.
Now the boat displaces only `W × 1 cm^(3)` of water. If
`rho` be the density of stones, the volume of water displaced by stones `= w//rho cm^(3)`
As `rho > 1`, hence `w//rho < w`, thus we have Now `(W + w//rho) < (W + w)` This shows that the volume of water displaced in the second case is less than the volume of water displaced in the first case. Hence the level of water will come down.