A vessel contains oil (density = 0.8 ; g/cm^3 | vedclass

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(C) As the sphere floats in the liquid,its weight is equal to the total upthrust force acting on it.Let $V$ be the total volume of the sphere and $\rh

Vedclass · Accepted Answer

$7.2$

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(C) As the sphere floats in the liquid,its weight is equal to the total upthrust force acting on it.Let $V$ be the total volume of the sphere and $ho$ be its density.Weight of the sphere = $V ho g$Upthrust due to oil = (Volume in oil) $	imes$ (Density of oil) $	imes g = (V/2) 	imes 0.8 	imes g = 0.4 Vg$Upthrust due to mercury = (Volume in mercury) $	imes$ (Density of mercury) $	imes g = (V/2) 	imes 13.6 	imes g = 6.8 Vg$Total upthrust = $0.4 Vg + 6.8 Vg = 7.2 Vg$Equating weight and total upthrust:$V ho g = 7.2 Vg$$ho = 7.2 \; g/cm^3$

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

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