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Question

A metallic sphere floats in an immiscible mixture of water (density 103 kg/m3) and a liquid (density 8×103kg/m3) such that its (23) part is in water and (13) part in the liquid. The density of the metal is


A

50003kg/m3

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B

100003kg/m3

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C

5000kg/m3

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D

2000kg/m3

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Solution

The correct option is B

100003kg/m3


Obviously water will float on top of the liquid. If the total volume of the ball is V from free body diagram

mg=FB+FBq

let density of water be ρω, density of liquid be ρl and density of ball be ρ.

ρ Vg=ρl13V g+ρω23V g

ρ=13ρl+23ρω

=13(8000)+23(1000)

=100003


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