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A vessel contains oil (density = 0.8 g/cm³) floating on top of mercury (density = 13.6 g/cm³). A homogeneous sphere floats with exactly half its volume submerged in mercury and the other half in oil. What is the density of the material of the sphere in g/cm³?

1. 3.3
2. 6.4
3. 7.2
4. 10.8

Correct answer: 7.2

Solution

Equating weight to total buoyant force: rho_sphere = (rho_mercury + rho_oil)/2 = (13.6 + 0.8)/2 = 14.4/2 = 7.2 g/cm³.

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