relative densities

Meaning: Density is mass per volume. Comparing the object's average density with the fluid's tells you whether the buoyant force (the weight of displaced fluid) can balance the object's weight. If the object is denser, a fully submerged object sinks. If it is less dense, it rises and floats partly submerged. If the densities are equal, it hangs suspended (neutrally buoyant). Specific gravity is a substance's density divided by the density of water (about 1000 kg/m³), so it has no units.

Equation: Vsub/Vtotal = ρobject/ρfluid, from setting the buoyant force equal to the weight, ρfluid Vsub g = ρobject Vtotal g. Here Vsub is the submerged volume (m³), Vtotal is the object's volume (m³), ρ is density (kg/m³), and g is gravitational acceleration (9.8 m/s²).

On the MCAT: Expect ice floating in water (ice is slightly less dense, so most of it is submerged), or a block moved from fresh water to denser salt water. In the second case the block rides higher, the submerged fraction falls, and the buoyant force stays equal to its weight. Another common setup gives apparent weight in air and in water and asks for specific gravity.

Common confusion: Students think size or mass decides sinking. Density decides it: a large log floats while a small pebble sinks. A floating object's buoyant force equals its weight, so it does not change when the fluid's density changes. Only the submerged volume changes.