The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

$A$ soap bubble (surface tension $= T$) is charged to a maximum surface density of charge $= \sigma$. When it is just about to burst,its radius $R$ is given by:

The excess of pressure inside a soap bubble compared to the outer pressure is:

The lower end of a capillary tube of diameter $2.00 \; mm$ is dipped $8.00 \; cm$ below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at the temperature of the experiment is $7.30 \times 10^{-2} \; N m^{-1}$. Atmospheric pressure $= 1.01 \times 10^{5} \; Pa$,density of water $= 1000 \; kg m^{-3}$,$g = 9.80 \; m s^{-2}$. Also,calculate the excess pressure.

When a large bubble rises from the bottom of a lake to the surface,its radius doubles. If atmospheric pressure is equal to that of a column of water of height $H$,then the depth of the lake is:

$216$ small identical liquid drops,each of surface area $A$,coalesce to form a bigger drop. If the surface tension of the liquid is $T$,what is the energy released in the process (in $AT$)?