Floating wood block: submerged volume ratio

A wooden block of density 0.75 g/cm³ floats in water of density 1.0 g/cm³. What fraction of its volume is submerged?

Step-by-step

1. V_sub/V = ρ_object/ρ_fluid = 0.75/1 = 75%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.75 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

Floating means the upthrust equals the weight: ρ_water × V_submerged = ρ_block × V_total, so the submerged fraction is ρ_block ÷ ρ_water.

Common mistakes

• Dividing 1.0 by 0.75 instead of 0.75 by 1.0.
• Thinking the submerged fraction depends on the size of the block.

Related

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