A cube of side 4cm is just completely immersed in liquid A. When it is put in liquid B, it floats with 2 cm outside the liquid. Calculate the ratio of densities of two liquids.

Dear Student

Let density of liquid A is ρA and  density of liquid B is ρBVolume of cube = 4×4×4=64 cm3When cube is completely immersed then the weight of displaced liquid is equal to weight of cube64ρAg= MgM=64ρAWhen liquid floats with 2 cm outside the liquid then voluem od immersed cube =2×2×2= 8 cm3So8ρBg= Mg8ρB= MEquating both equations64ρA=8ρBρAρB=864=18
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