A soap bubble, having radius of $1 ext{ mm}$, is blown from a detergent solution having a surface tension of

Question

A soap bubble, having radius of $1	ext{ mm}$, is blown from a detergent solution having a surface tension of $2.5 	imes 10^{-2}	ext{ N/m}$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g = 10	ext{ m/s}^2$, density of water $= 10^3	ext{ kg/m}^3$, the value of $Z_0$ is :

Accepted Answer

Excess pressure $= \frac{4T}{R}$, Gauge pressure $= ho g Z_0$. $P_0 + \frac{4T}{R} = P_0 + ho g Z_0$. $Z_0 = \frac{4T}{R 	imes ho g} = \frac{4 	imes 2.5 	imes 10^{-2}}{10^{-3} 	imes 1000 	imes 10}	ext{ m} = 1	ext{ cm}$.

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