A soap bubble having radius of 1 m m is blown from a detergent solution having a surface tension of 2.5 × 10 - 2 N m - 1 . The pressure inside the bubble equals at a point Z 0 below the free surface o

Question

A soap bubble having radius of 1 m m is blown from a detergent solution having a surface tension of 2.5 × 10 - 2 N m - 1 . 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 k g m - 3 , the value of Z 0 isNEET 2019 (All India)

TestHub · Accepted Answer

Pressure inside soap bubble is given by, $∆ P = \frac{4 T}{R}$
Pressure below water surface at depth $Z_{0}$ is given by, $∆ P = ρ g Z_{0}$
According to question,
$\Rightarrow \frac{4 T}{R} = ρ g Z_{0}$
$\Rightarrow Z_{0} = \frac{4 T}{ρ g} = \frac{4 \times 2.5 \times 10^{- 2}}{10^{3} \times 10 \times 10^{- 3}}$
$\Rightarrow Z_{0} = \frac{1}{100} m$
$\Rightarrow Z_{0} = 1 c m$

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