Floating plastic block: submerged fraction

A plastic block of density 0.5 g/cm³ floats in water of density 1.0 g/cm³. What fraction of its total volume is submerged?

Step-by-step

1. V_sub/V = ρ_object/ρ_fluid = 0.5/1 = 50%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.5 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

A floating body is in balance, so the upthrust equals its weight: ρ_water × V_submerged = ρ_block × V_total. The submerged fraction is therefore the block's density divided by the water's density, independent of how big the block is.

Common mistakes

• Dividing the water density by the block density instead of the other way round.
• Thinking a larger block would submerge a larger fraction of itself.

Related

buoyancy-float buoyancy-wood-block-float-ratio buoyancy-iceberg-submerged-fraction