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A hemispherical bowl just floats (on the verge of sinking) in a liquid of density 1.2 x 10³ kg/m³. The outer diameter of the bowl is 1 m and the material of the bowl has density 2 x 10⁴ kg/m³. Find the inner diameter of the bowl.
- 0.98 m
- 0.5 m
- 1.91 m
- 1.75 m
Correct answer: 0.98 m
Solution
On the verge of sinking the whole outer hemisphere is submerged. Weight = buoyancy: rho_b (2/3)pi(R³ - r³) = rhoₗ (2/3)pi R³ => (R³ - r³) rho_b = R³ rhoₗ => r³ = R³(1 - rhoₗ/rho_b). With R = 0.5, rhoₗ/rho_b = 1.2e3/2e4 = 0.06: r³ = 0.125 x 0.94 = 0.1175, r = 0.4898 m, inner diameter = 0.98 m.
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