The excess pressure inside the first soap bubble is three times that of a second soap bubble. What is the ratio of the volumes of the first bubble to the second bubble?

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:

When a big drop of water is formed from $n$ small drops of water,the energy loss is $3E$,where $E$ is the energy of the bigger drop. The radius of the bigger drop is $R$ and that of the smaller drop is $r$. Then the value of $n$ is:

Energy needed in breaking a drop of radius $R$ into $n$ drops of radii $r$ is given by

If the excess pressure inside a soap bubble of radius $3 \,mm$ is equal to the pressure of a water column of height $0.8 \,cm$, then the surface tension of the soap solution is ( $\rho_{\text{water}} = 1000 \,kg/m^3, g = 9.8 \,m/s^2$ ).

Let $n$ be the number of liquid drops,each with surface energy $E$. These drops join to form a single drop. In this process: