First slide

Surface tension

Question

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5 \times 10^{- 2} N / m$ . 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 water $10^{3} kg / m^{3}$ , the value of $Z_{0}$ is

Difficult

A

0.5 cm
B

100 cm
C

10 cm
D

1 cm

Solution

$The pressure at a point Z_{0} below the surface of water, P_{Z_{0}} = P_{0} + {ρgZ}_{0} Also, pressure inside a soap bubble, P = P_{0} + \frac{4 T}{R} As per question, P_{Z_{0}} = P Z_{0} = \frac{4 T}{Rρg} = \frac{4 \times 2.5 \times 10^{- 2}}{1 \times 10^{- 3} \times 10^{3} \times 10} = 1 \times 10^{- 2} m = 1 cm$

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