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

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(C) Let $V$ be the total volume of the sphere and $\rho$ be the density of the material of the sphere.Since the sphere is floating,its weight must be

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$7.2$

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(C) Let $V$ be the total volume of the sphere and $ho$ be the density of the material of the sphere.Since the sphere is floating,its weight must be equal to the total buoyant force (upthrust) acting on it.Weight of the sphere $= V ho g$Buoyant force due to oil $= (V/2) 	imes ho_{oil} 	imes g = (V/2) 	imes 0.8 	imes g = 0.4 Vg$Buoyant force due to mercury $= (V/2) 	imes ho_{Hg} 	imes g = (V/2) 	imes 13.6 	imes g = 6.8 Vg$Equating the weight to the total buoyant force:$V ho g = 0.4 Vg + 6.8 Vg$$V ho g = 7.2 Vg$$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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