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Topic: Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise· Properties of Solids and Liquids

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 Z_0 below the free surface of water in a container. Taking g = 10 m/s^2, density of w…

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of \(2.5\times10^{-2}\) N/m. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of water in a container. Taking \(g = 10\) m/s\(^2\), density of water \(= 10^3\) kg/m\(^3\), the value of \(Z_0\) is :

1. 100 cm

2. 10 cm

3. 1 cm

4. 0.5 cm

1 answer

Best answer

Answer: 3. 1 cm

A soap bubble has two surfaces, so the excess pressure inside is \(\Delta P=\dfrac{4T}{R}\).

\(\Delta P=\dfrac{4\times2.5\times10^{-2}}{10^{-3}}=100\ \text{Pa}\).

At depth \(Z_0\) in water the pressure above atmospheric is \(\rho g Z_0\). Equate: \(10^3\times10\times Z_0=100\).

\(Z_0=10^{-2}\) m \(=1\) cm.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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