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

Two soap bubbles of radius $2 \ cm$ and $4 \ cm$,respectively,are in contact with each other. The radius of curvature of the common surface,in $cm$,is . . . . . . .

When an air bubble rises from the bottom of a deep lake to a point just below the water surface,the pressure of air inside the bubble

$A$ spherical liquid drop splits into $729$ identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of the resulting drops,then $\frac{E}{U} = \frac{1}{x}$. The value of $x$ is

The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal condition,they combine with each other to form a single bubble. The radius of the resultant bubble is

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