Question

I am working on a problem that reads as follows: “Salt water has grater density than fresh water. A boat floats in both fresh water and salt water. Where is the buoyant force greater on the boat”. The answer is that the buoyant force is the same in both, but I don’t really understand why. One of the equations we were given is Buoyant Force = density of the fluid * volume displaced * 9.81 m/s^2. So if the densities are different, shouldn’t the bouyant force be greater when the boat is in salt water?

Answer 1

look in both fresh water and salt water ,boat remains at rest and is in equilibrium

therefore weight of the boat will be balanced by the buoyant force,as the weight of boat will remain same in both fresh and salt water,therefore buoyant force will also be same in both the cases

however,since buoyant force is same in both the cases,volume submerged in case of salt water will be less as salt water's density is greater .