Physics Question on mechanical properties of fluid

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 $g = 1 0 m / s ^{2}$ , density of water $= 1 0 ^{3} kg / m ^{3}$ , the value of $Z _{0}$ is:

Answer 1

Solution

Excess pressure = $\frac{4T}{R}$ , Gauge pressure $= \rho g Z_0$
$P_{0} + \frac{4T}{R} = P_{0} + \rho qZ_{0}$
$Z_{0} = \frac{4T}{R \times\rho g}$
$Z_{0} = \frac{4\times2.5 \times10^{-2}}{10^{-3} \times1000 \times10} m$
$Z_0 = 1 \; cm$