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

3.3

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7.2

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Solution

The correct option is C 7.2
$ρ_{0} \frac{v}{2} g + ρ_{H g} \frac{v}{2} g = ρ_{s} . v . g$
$∴$ $ρ_{s} = \frac{ρ_{0} + ρ_{H g}}{2} = \frac{7.2 g}{c c}$

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A vessel contains oil (ρ=0.8gmcm3) over mercury (ρ=13.6gmcc). A homogenous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere is _____ gmcc.

The correct option is C 7.2ρ0v2g+ρHgv2g=ρs.v.g ∴ ρs=ρ0+ρHg2=7.2gcc

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

The correct option is C 7.2
$ρ_{0} \frac{v}{2} g + ρ_{H g} \frac{v}{2} g = ρ_{s} . v . g$
$∴$ $ρ_{s} = \frac{ρ_{0} + ρ_{H g}}{2} = \frac{7.2 g}{c c}$