Question

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

• A. $100cm$
• B. $10cm$
• C. $1cm$
• D. $0.5cm$

Answer 1

The correct option is C $1cm$

$P=P_0+\rho g{Z}_0.........\left(i\right)P=P_0+\frac{4T}{R}...........\left(ii\right)\rho g{Z}_0=\frac{4T}{R}\therefore Z_0=\frac{4T}{\rho gR}=\frac{4\times 2.5\times {10}^{-2}}{{10}^3\times 10\times {10}^{-3}}={10}^{-2}=1cm$