Q. A solid sphere of volume and density floats at the interface of two immiscible liquids of densities and respectively. If < < , then the ratio of volume of the parts of the sphere in upper and lower liquid is

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Solution:

V = Volume of solid sphere.
Let V₁ = Volume of the part of the sphere immersed in a liquid of density and V₂ = Volume of the part of the sphere immersed in liquid of density .
According to law of floatation,

and
Hence from eqns (i) and (ii),

or
or

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