Two soap bubbles of radii $r_1 = 4 \ cm$ and $r_2 = 5 \ cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface is...... $cm$.

$A$ soap bubble of radius $3 \, cm$ is formed inside another soap bubble of radius $6 \, cm$. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... $cm$.

When two soap bubbles of radii $4 \, cm$ and $5 \, cm$ coalesce,what is the radius of the common interface surface in $cm$?

$A$ soap bubble has radius $R$ and thickness $d$ $(d \ll R)$ as shown. It collapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is

Two soap bubbles of radii $3r$ and $4r$ are in contact with each other. The radius of curvature of the interface between the bubbles is:

$A$ vessel,whose bottom has round holes with a diameter of $0.1 \, mm$,is filled with water. The maximum height to which the water can be filled without leakage is ....... $cm$ (Surface Tension of water = $75 \, dyne/cm$,$g = 1000 \, cm/s^2$).