Question

An empty cylindrical drum 1 metre long and 0.6 m. in diameter has mass 20 kg. Find the mass which must be placed in it so that it will float with half of its volume immersed in (a) salt water and (b) fresh water.

Answer 1

The densities of freshwater and saltwater will be designated by ρ_f=1000kg/m³ and ρ_s=1025kg/m³ respectively. Volume V of the drum=πr²h where r=radius=0.3m, h=height (length)=1m. V=0.09π m³. If M=the mass of the contents, the total mass of the filled drum=20+M kg. This is also the mass of water displaced. Volume of the water displaced depends on the density ρ of the water=mass/volume, so the volume v of water=mass/ρ m³=(20+m)/ρ. This volume has to equal V/2 so that the drum floats with half its volume submerged. Therefore V/2=(20+M)/ρ.

M=ρV/2-20=0.045πρ-20=0.1414ρ-20 kg approx.

(a) ρ=ρ_s=1025kg/m³: M=124.91 kg.

(b) ρ=ρ_f=1000kg/m³: M=121.37 kg.