A water drop of radius 1.5 mm falls from a height of 1 km. Its drag coefficient is 0.5, water density is 1000 kg/m³ and air density is 1.29 kg/m³. Find its terminal velocity (take g ≈ 9.8 m/s²).
Options

Question

A water drop of radius 1.5 mm falls from a height of 1 km. Its drag coefficient is 0.5, water density is 1000 kg/m³ and air density is 1.29 kg/m³. Find its terminal velocity (take g ≈ 9.8 m/s²).

G1 Physics · Accepted Answer

Step 1: At terminal speed, net weight = aerodynamic drag: (4/3)πr³(ρw − ρa)g = ½Cᴅρaπr²vₜ². Step 2: Solve: vₜ² = 8r(ρw − ρa)g/(3Cᴅρa). Step 3: Substitute r = 1.5 × 10⁻³ m, ρw = 1000, ρa = 1.29 kg/m³, Cᴅ = 0.5, g = 9.8 m/s². Step 4: vₜ² = [8 × 1.5 × 10⁻³ × (1000 − 1.29) × 9.8]/[3 × 0.5 × 1.29] ≈ 60.7. Step 5: vₜ ≈ √60.7 = 7.79 m/s. Final answer: 7.8 m/s (Option B).