Floating wax block: submerged fraction

A wax block of density 0.8 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 = 0.8/1 = 80%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.8 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

Floating means the upthrust balances the weight, so ρ_water × V_submerged = ρ_block × V_total. The submerged fraction is the block's density divided by the water's density.

Common mistakes

• Working out 1.0 ÷ 0.8 instead of 0.8 ÷ 1.0.
• Answering 0.2 (the part above the surface) when the submerged part is asked for.

Related

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