Floating block: what fraction is submerged?

A wooden block of density 0.6 g/cm³ floats in water. What fraction of its volume is submerged?

Step-by-step

1. V_sub/V = ρ_object/ρ_fluid = 0.6/1 = 60%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.6 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

A floating object displaces its own weight, which gives ρ_water·V_submerged = ρ_object·V_total. So the submerged fraction is the density ratio.

Common mistakes

• Using the volume ratio instead of the density ratio.
• Forgetting that the fraction is of the total volume.

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