Question

A boat full of scrap iron is floating on water in a lake. If all the iron is dropped into water the water level will: (a) go up (b) remain the same (c) rise very high (d) fall down

Answer 1

The stones occupy some volume and weight thus displace some amount of water when placed in boat or when unloaded in water. Now, when the stones are on the boat the volume occupied by them will be greater than when they are in water. This s what causes the water level to drop as they are unloaded.

Lets see how...

The volume of water displaced when stones are in boat will be

dV = (mboat + mstones)/ρwater

(as volume = mass/density)

here,

mboat is the mass of the boat and mstones is the mass of the stones

and ρwater is the density of water = 1 gm/cc

so,

dV = mboat + mstones

now, 

The volume of water displaced when stones are in boat will be

dV = (Wboat/ρwater)+ (Wstones/ρstones)

so,

dV' = mboat + (mstones/ρstones)

here

 ρstones is the density of stones which is greater than 1 gm/cc.

so,

dV > dV'

thus, volume displaced in the first case will be more than that of the second case.

Answer 2

The level of the water will be decreased or fall down because according to the Archimedes principle the weight of the liquid displaced is equal to the weight of the substance or body in the container