A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 10⁻² N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z₀ is:

Question

Accepted Answer

10 cm. The excess pressure inside a soap bubble is given by ΔP = 4T/r, where T is the surface tension and r is the radius. Substituting the values, ΔP = (4 × 2.5 × 10⁻²) / (1 × 10⁻³) = 100 Pa. The pressure at depth Z₀ in water is given by P = ρgZ₀. Equating ΔP = ρgZ₀, we get Z₀ = ΔP / (ρg) = 100 / (10³ × 10) = 0.01 m = 10 cm.

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 10⁻² N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z₀ is:

Solution

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