Question

1. A ship has an area of cross section at the water line 200m, by what depth does the ship sink in fresh water when it loads a cargo of 4000 tones

b) if the ship and the cargo has a displacement turnage of 123000 tones , by what amount will the ship rise in the water ,when it sails from fresh water into Sea water

Density of Sea water 1025m

Answer 1

1)

$\frac{m}{\rho}=Sh,\implies h=\frac{m}{\rho S},$

$h=\frac{4\cdot 10^6}{1025\cdot 200}=19.5~m,$

$2) \Delta h=\frac{M}{S}(\frac{1}{\rho_1}-\frac {1}{\rho}),$

$\Delta h=\frac{123\cdot 10^6}{200}\cdot (\frac{1}{1000}-\frac{1}{1025})=15~m.$