Hydrostatic balance with linear density profile

Steps:

• Model density as ρ(h) = ρ₀ (1 - h/H), where ρ₀ = 1.3 kg/m³ and H is height to zero density.
• Surface pressure P₀ = 100 kPa balances weight of air column: P₀ = g ∫₀^H ρ(h) dh = g ρ₀ H / 2, with g ≈ 9.8 m/s².
• Rearrange: H = 2 P₀ / (g ρ₀).
• Compute: H = 2 × 100,000 / (9.8 × 1.3) ≈ 15,700 m ≈ 16 km.

Why B is correct:

• Derives directly from hydrostatic equation for linear density tapering to zero at H.

Why the others are wrong:

• A. Underestimates by halving the effective column mass.
• C. Overestimates by assuming constant density instead of linear decrease.
• D. Far exceeds scale based on surface pressure and density.

Final answer: B