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
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