Question

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:

(a) 100 cm

(b) 10 cm

(c) 1 cm

(d) 0.5 cm

Answer 1

Correct option is : (c) 1 cm

Excess pressure = \(\frac{4T}{R}\), gauge pressure = ρgz₀

P₀ + \(\frac{4T}{R}\) = ρ₀ + ρgz₀

z₀ = \(\frac{4T}{R\times\rho g}\)

z₀ = \(\frac{4\times2.5\times10^{-2}}{10^{-3}\times100\times10}m\)

z₀ = 1 cm