A cubical block of density ρb = 600 kg/m³ floats in a liquid of density ρe = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part i $s _____$ cm.
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Question

A cubical block of density ρb = 600 kg/m³ floats in a liquid of density ρe = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part i s _____ cm.

G1 Physics · Accepted Answer

For a floating body, weight = buoyant force. If A is the horizontal cross-sectional area and h is the submerged height, ρ(block)AHg = ρ(liquid)Ahg. Therefore, h = [ρ(block)/ρ(liquid)]H. Substitute: ρ(block) = 600 kg/m³, ρ(liquid) = 900 kg/m³, H = 8.0 cm. Hence, h = (600/900)×8 = (2/3)×8 = 16/3 cm ≈ 5.3 cm. Correct option: D.