Question bank/JEE Main/Physics

Two liquids of densities 1 are mixed in equal
volumes. A cube of external dimension 20 cm has an inner cubical portion
of side 10 cm whose density is twice that of the outer portion. If this
cube is just floating in the liquid mixture, find the density of the
inner portion.

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ρ = [IMAGE] = 2 mg = 2ρ1 × 103 + ρ1 × (203 - 103)
= 9ρ1 × 103 g = ρ × 8 × 103 g

Source: Grass-G / P-01 Physics Paper-01_Update.docx