A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of . The pressure inside the bubble equals that at a point below the free surface of water in a container. Taking , density of water , the value of is

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Solution

Q.
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 that 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 [2019]

1 0.5 cm

2 100 cm

3 10 cm

4 1 cm

Ans.
(4)

The pressure at a point $Z_{0}$ below the surface of water, $P_{Z_{0}} = P_{0} + ρ g Z_{0}$

Also, pressure inside a soap bubble, $P = P_{0} + \frac{4 T}{R}$

As per question, $P_{Z_{0}} = P$ $∴$ $P_{0} + \frac{4 T}{R} = P_{0} + ρ g Z_{0}$

$Z_{0} = \frac{4 T}{R ρ g} = \frac{4 \times 2.5 \times 10^{- 2}}{1 \times 10^{- 3} \times 10^{3} \times 10} = 1 \times 10^{- 2} m = 1$ $cm$

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