The excess pressure inside a soap bubble $A$ in air is half the excess pressure inside another soap bubble $B$ in air. If the volume of the bubble $A$ is $n$ times the volume of the bubble $B$,then the value of $n$ is . . . . . . .

If a soap bubble expands, the pressure inside the bubble:

$A$ long cylindrical glass vessel has a pinhole of diameter $0.2 \,mm$ at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water,$T=0.07 \,N/m$,acceleration due to gravity,$g=10 \,m/s^2$) (in $\,cm$)

$A$ capillary type tube $AB$ is connected to a manometer $M$ as shown in the figure. Stopper $S$ controls the flow of air. $AB$ is dipped into a soap solution where surface tension is $T$. On opening the stopper for a while,a bubble is formed at $B$ end of the manometer and the level difference in manometer limbs is $h$. If $\rho$ is the density of the soap solution and $r$ is the radius of curvature of the bubble,then the surface tension $T$ of the liquid is given by:

Two small drops of mercury each of radius $r$ coalesce to form a single large drop of radius $R$. The ratio of the total surface energies before and after the change is

If the radius of a soap bubble is four times that of another,then the ratio of their excess pressures will be