Two soap bubbles of radii $2 \, cm$ and $4 \, cm$ join to form a double bubble in air. The radius of curvature of the interface is .......... $cm$.

$A$ liquid drop of volume $V$ is placed on the surface of a glass plate. Then,another glass plate is placed on it such that the liquid forms a thin layer of area $A$ between the surfaces of the two plates. To separate the plates,a force $F$ has to be applied normal to the surfaces. The surface tension of the liquid is

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

Fill in the blanks:
$(i)$ $A$ bubble in water has .......... free surface.
$(ii)$ $A$ bubble in air has .......... free surface.
$(iii)$ $A$ rain drop has .......... free surface.

The excess pressure due to surface tension in a spherical liquid drop of radius $r$ is directly proportional to

$A$ certain number of spherical liquid drops of radius $r$ coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid,which one of the following statements is true for the energy $(E)$ in the process?