Archimedes' Principle for Floating Equilibrium

Steps:

• Fraction of cube submerged = 100% - 42% = 58% or 0.58.
• Weight of cube = buoyant force, so ρ_iron × V × g = ρ_mercury × (0.58V) × g.
• Cancel V and g: ρ_iron = ρ_mercury × 0.58.
• ρ_mercury = 7900 / 0.58 ≈ 13620 kg/m³, closest to 14000 kg/m³.

Why C is correct:

• Matches the calculated density (7900 / 0.58 ≈ 13620 kg/m³), as fraction submerged equals object density divided by fluid density per Archimedes' principle.

Why the others are wrong:

• A: 7900 / 3000 ≈ 2.63 (>1), implies over 100% submerged, impossible for floating.
• B: 7900 / 4300 ≈ 1.84 (>1), implies over 100% submerged, impossible.
• D: 7900 / 19000 ≈ 0.416 (41.6% submerged), implies 58.4% above surface, not 42%.

Final answer: C