Archimedes' Principle for Floating Iceberg

Steps:

• Weight of iceberg equals buoyant force: ρ_i g (π r² H) = ρ_w g [π r² (H - h)].
• Cancel common terms: ρ_i H = ρ_w (H - h).
• Rearrange: ρ_w h = ρ_w H - ρ_i H.
• Solve: h = H (ρ_w - ρ_i)/ρ_w.

Why A is correct:

• Matches the equilibrium condition from Archimedes' principle, where h is the unsubmerged fraction proportional to the density difference.

Why the others are wrong:

• B: Represents submerged height fraction ρ_i/ρ_w, not above-water height.
• C: Exceeds H since ρ_w > ρ_i, impossible for floating object.
• D: Identical to B, incorrectly gives submerged fraction.

Final answer: A