A soap bubble of radius 1 mm is formed with detergent surface tension 2.5 × 10⁻² N/m. Its internal pressure equals the pressure of water at depth Z₀ below a free water surface. Take g = 10 m/s² and ρwater = 10³ kg/m³. Find Z₀.
Options

Question

A soap bubble of radius 1 mm is formed with detergent surface tension 2.5 × 10⁻² N/m. Its internal pressure equals the pressure of water at depth Z₀ below a free water surface. Take g = 10 m/s² and ρwater = 10³ kg/m³. Find Z₀.

Options

G1 Physics · Accepted Answer

Step 1: Excess pressure in a spherical soap bubble (two surfaces) is ΔP = 4T/r. Step 2: Substitute T = 2.5 × 10⁻² N/m, r = 1 mm = 10⁻³ m. Step 3: ΔP = 4 × 2.5 × 10⁻²/(10⁻³) = 100 Pa. Step 4: Hydrostatic excess pressure at depth Z₀ is ρgZ₀. Step 5: 100 = 1000 × 10 × Z₀ ⟹ Z₀ = 0.01 m = 1 cm. Final answer: Z₀ = 1 cm (Option C).