Question

mason notices that his boat sinks lower into the water in a freshwater lake than in the ocean. what could explain this?

the boat is more dense in salt water.
the boat is less dense in salt water.
salt water is less dense than freshwater
salt water is more dense than freshwater.

Explanation:

According to Archimedes' principle, the buoyant force \(F_b=
ho Vg\), where \(
ho\) is the density of the fluid, \(V\) is the volume of the fluid displaced, and \(g\) is the acceleration due to gravity. The weight of the boat \(W = mg\) is constant. In equilibrium, \(F_b=W\). Since \(W\) is the same in both freshwater and salt - water, and \(g\) is constant. If \(
ho_{salt - water}>
ho_{freshwater}\), then from \(F_b=
ho Vg\), \(V_{freshwater}>V_{salt - water}\) (because to keep \(F_b = W\) constant, when \(
ho\) increases, \(V\) decreases). So the boat sinks lower (displaces more water) in freshwater because salt - water is more dense than freshwater.

Answer:

Salt water is more dense than freshwater.