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

Moderate

A

0.5 cm
B

100 cm
C

10 cm
D

1 cm

Solution

Pressure inside soap bubble = $P_{0} + \frac{4 T}{R}$
Pressure at a point $z_{0}$ below surface of water = $P_{0} + {ρgZ}_{0}$
$P_{0} =$ atmospheric pressure
$P_{0} + \frac{4 T}{R} = P_{0} + {ρgz}_{0}$
$\frac{4 T}{R} = {pgZ}_{0}$
$Z_{0} = \frac{4 T}{ρgR}$
$Z_{0} = \frac{4 \times 2.5 \times 10^{- 2}}{10^{3} \times 10 \times 1 \times 10^{- 3}}$
$Z_{0} = 1 cm$

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