Three small identical bubbles of water having the same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is:

When an air bubble rises from the bottom of a deep lake to a point just below the water surface,the pressure of air inside the bubble

If the surface tension of a soap solution is $0.03 \, N/m$,then the excess pressure inside a soap bubble of diameter $6 \, mm$ over the atmospheric pressure will be:

Two small drops of liquid of same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is

An air bubble of radius $0.1 \ cm$ lies at a depth of $20 \ cm$ below the free surface of a liquid of density $1000 \ kg/m^3$. If the pressure inside the bubble is $2100 \ N/m^2$ greater than the atmospheric pressure,then the surface tension of the liquid in $SI$ unit is (use $g=10 \ m/s^2$)

The excess pressure inside a soap bubble is $1.5$ times the excess pressure inside a second soap bubble. The volume of the second bubble is '$x$' times the volume of the first bubble. The value of '$x$' is