A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank is:
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A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank is:

G1 Physics · Accepted Answer

Let density of water be ρ. Density of material of the sphere: = σρ For just floating: Weight = buoyant force σρg × (π/6)(D³ - d³) = ρg × (π/6)D³ Cancel common terms: σ(D³ - d³) = D³ Therefore: σD³ - σd³ = D³ (σ - 1)D³ = σd³ Hence: D³/d³ = σ/(σ - 1) Therefore: D/d = [σ/(σ - 1)]¹ᐟ³