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

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

Mechanical Properties of Fluids

Solution:

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Weight $=$ Buoyant force
$V \rho_{m} g=\frac{V}{2} \rho_{ Hg } g+\frac{V}{2} \rho_{ oil } g$
$\rho_{m}=\frac{\rho_{ Hg }+\rho_{ oil }}{2}$
$=\frac{13.6+0.8}{2}=\frac{14.4}{2}=7.2\, g / cm ^{3}$