A ship sails from seawater (specific gravity 1.025) into fresh water and therefore sinks slightly. When its load of 600,000 kg is removed, it returns to its original level. Assuming that the sides of the ship are vertical at the water line, find the mass of the ship before it was unloaded.

A ship sails from seawater (specific gravity 1.025) into fresh water and therefore sinks slightly. When its load of 600,000 kg is removed, it returns to its original level. Assuming that the sides of the ship are vertical at the water line, find the mass of the ship before it was unloaded.

1 Approved Answer

Nethi C answered on January 11, 2021

5 Ratings,(9 Votes)

 Floating at the same level means displacing the same amount of water. 

Let M1 = the mass of the ship and M2 be the mass of the cargo, and V be the volume displaced at the original floating level of the ship. 

Then M1 + M2 = V*1025. The mass of the ship with cargo is equal to the mass of volume V of sea water (density 1025 kg/m^3) 

M1 = V*1000. The mass of the unloaded ship is equal to the mass of volume V of fresh water (density 1000 kg/m^3). 

I can solve for V = M1/1000 and substitute into the first equation 

M1 + M2 = (M1/1000) * 1025 = 1.025*M1 

I know M2 = 430000 kg. So I can solve for M1.