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 . . . . . . .

$A$ 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 $\,cm$)

Consider an air bubble of radius $2 \,mm$ in a liquid at a depth of $5 \,cm$ below the free surface. The density of the liquid is $1000 \,kg/m^3$ and the surface tension is $0.1 \,N/m$. Find the pressure inside the air bubble relative to the pressure at the free surface of the liquid. (Take $g = 10 \,m/s^2$) (in $\,Pa$)

One large soap bubble of diameter '$D$' breaks into $64$ smaller bubbles of equal size. If the surface tension of the soap solution is '$T$',what is the change in surface energy (in $\pi T D^2$)?

The excess pressure in a soap bubble is double that in another one. The ratio of their volumes is .............

The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble must be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is $(\varepsilon_0 = \text{permittivity of the free space})$