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Q.

A solid sphere having volume V and density ρ floats at the interface of two immiscible liquids of densities ρ1 and ρ2 respectively. lf ρ1<ρ <ρ2, then the ratio of volume of the parts of the sphere in upper and lower liquid is

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a

ρ-ρ1ρ2-ρ

b

ρ2-ρρ-ρ1

c

ρ+ρ1ρ+ρ2

d

ρ+ρ2ρ+ρ1

answer is B.

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Detailed Solution

According to law of flotation,Vρg = V 1ρ1g+V2ρ2g------(i)and V = V1 + V2----(ii)Hence from Eqs. (i) and (ii),V1ρg + V2ρg = V1ρ1g+V2ρ2gOr V1(ρ-ρ1)g = V2(ρ2-ρ) or V1V2 = ρ2-ρρ-ρ1
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A solid sphere having volume V and density ρ floats at the interface of two immiscible liquids of densities ρ1 and ρ2 respectively. lf ρ1<ρ <ρ2, then the ratio of volume of the parts of the sphere in upper and lower liquid is