(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

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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 $\rho$ be its density.Weight of the sphere = $V \rho g$Upthrust due to oil = (Volume in oil) $\times$ (Density of oil) $\times g = (V/2) \times 0.8 \times g = 0.4 Vg$Upthrust due to mercury = (Volume in mercury) $\times$ (Density of mercury) $\times g = (V/2) \times 13.6 \times g = 6.8 Vg$Total upthrust = $0.4 Vg + 6.8 Vg = 7.2 Vg$Equating weight and total upthrust:$V \rho g = 7.2 Vg$$\rho = 7.2 \; g/cm^3$

Class 11 Physics Fluid Mechanics and Surface Tension Buoyancy, Archimedes' Principle and Laws of Floatation

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$A$ 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:

IIT 1998 All IIT

A
$3.3$
B
$6.4$
C
$7.2$
D
$12.8$

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Fluid Mechanics and Surface Tension

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Buoyancy, Archimedes' Principle and Laws of Floatation

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$A$ 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:

Similar Questions

$A$ body floats in a liquid contained in a beaker. The whole system,as shown,falls freely under gravity. The upthrust on the body due to the liquid is

$A$ vessel filled with water is kept on a weighing pan and the scale is adjusted to zero. $A$ block of mass $M$ and density $\rho$ is suspended by a massless spring of spring constant $k$. This block is submerged into the water in the vessel. What is the reading of the scale?

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be:

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