a drum of mass 14kg when empty,is 75cm long,and 60cm in diameter.Find itss draft in salt water if it contains 200 litres of paraffin of relative density 0.63
mass of 1 liter of (pure) water is 1 kg
mass of 200 liter of water is 200 kg
mass of 200 liter of paraffin, of sg = 0.63, is 200*0.63 = 126 kg
Total weight of drum plus paraffin is 14 + 126 = 140 kg
If drum floats then it will displace 140 kg of (pure) water, which is 140 liters.
Displacement of drum is V = pi(D^2 / 4) * h, where V = 140 liters = 0.14 m^3, D = diameter = 60 cm = 0.6 m and h = ?
0.14 = pi(0.36/4)*h
h = 14/(9pi)
h = 0.495 m
h = 49.5 cm which is less than 75 cm, meaning the drum is floating.
However salt water has a sg = 1.025
Since salt water is denser than pure water, then less of it needs to be displaced to give 140 kg of upthrust.
Draft of drum in pure water = 49.5 cm
Draft of drum in salt water is 49.5/1.025 = 48.3 cm