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:

$A$ small soap bubble of radius $4 \ cm$ is trapped inside another bubble of radius $6 \ cm$ without any contact. Let $P_2$ be the pressure inside the inner bubble and $P_0$ be the pressure outside the outer bubble. The radius of another bubble with a pressure difference $P_2 - P_0$ between its inside and outside would be....... $cm$.

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 $g=10 \ m/s^2$)

Let $R_{1}$ and $R_{2}$ be the radii of two mercury drops. $A$ big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

$A$ drop of liquid of diameter $2.8\, mm$ breaks up into $125$ identical drops. The change in energy is nearly ........ $erg$ (Surface Tension of liquid = $75\, dynes/cm$).

Two soap bubbles with radii $r_1$ and $r_2$ $(r_1 > r_2)$ come in contact. Their common surface has a radius of curvature $r$. Find $r$.