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Buoyancy

A vessel cont...

Question

A vessel contains oil $(density = 0.8 g / c m^{3})$ over mercury $(density = 13.6 g / c m^{3})$ . A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density $(in g / c m^{3})$ of the material of sphere is

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Solution

Draw a diagram of given problem.
Calculate density of the material of the sphere.
Given,
Density of oil $d_{o} = 0.8 g / c m^{3}$
Density of mercury $d_{m} = 13.6 g / c m^{3}$
Half of the sphere immersed in the mercury and half remains in oil,
Using Archimedes’ principle,
$d V g = d_{0} \times \frac{V}{2} g + d_{m} \times \frac{V}{2} g$

$d = \frac{d_{0} + d_{m}}{2}$

$= \frac{0.8 + 13.6}{2} = 7.2$

Final answer: $(7.2)$

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