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Q.

A cylindrical block floats vertically in a liquid of density ρ1  kept in a container such that the fraction of volume of the cylinder inside the liquid is x1. Then some amount of another immiscible liquid at density ρ2(ρ2<ρ1)  is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquid with x2 fraction of volume at the cylinder inside the liquid of density ρ1.  The ratio of ρ1ρ2 will be

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a

1+x2x1+x2

b

1−x2x1−x2

c

1+x2x1−x2

d

1−x2x1+x2

answer is B.

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Detailed Solution

Given density of liquid =ρ1 The fraction of volume of cylinder inside the liquid=x1Density of liquid=ρ2 (ρ2<ρ1)From relation P=P1+P2 ρ1x1g=ρ1x2g+ρ2(1−x2)g  FB will be same in both casesFB means Buoyancy forceNow ρ1x1g=ρ1x2g+ρ2(1−x2)gρ1(x1−x2)=ρ2(1−x2)ρ1ρ2=(1−x2x1−x2)
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