Density and pressure — common mistakes

Remember the difference between density of the object and density of the fluid when calculating upthrust. Upthrust always depends on the density of the fluid displaced, not the object itself! Also, be careful to distinguish between gauge pressure ($\rho g h$) and absolute pressure ($p_{atm} + \rho g h$) in questions.

Pressure increases with depth in a fluid because the deeper you go, the greater the column of fluid above you. This increased column of fluid has more weight, and this weight is pushing down on the area below it, resulting in higher pressure.

Density is a property of a material, describing how much mass is contained within a specific volume. Pressure, on the other hand, describes how a force is distributed over a surface area. An object can be dense, but if its weight is spread over a large area, it might exert low pressure.

Archimedes' Principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. If this buoyant force is greater than or equal to the object's own weight, the object will float. If its weight is greater than the maximum possible buoyant force (when fully submerged), the object will sink. This is equivalent to comparing densities: an object floats if its average density is less than the fluid's density.