Question

A large tree trunk is floating in the sea. The density of the sea water is 1065 kg/m3, the density of the trunk is 715 kg/m3. What fraction of the trunk's volume is under the surface of the water?

Answer 1

Difference in densities = 1065 – 715 = 350 kg/m^3
The ratio of density of wood to that of water is 715/1065 = 0.671
If the ratio were = 1, then all the volume of wood will be inside the water surface.

Hence it is evident that (1 - 0.671) =0.329 of the volume of wood is exposed to air.


Let v be the volume exposed to air and V is the total volume of wood

Since the wood is floating mass of wood = mass of equal volume of water displaced.

V *715 = (V-v) 1065

v/V = 0.329