$A$ soap bubble is blown to a diameter of $7 \ cm$. $36960 \ erg$ of work is done in blowing it further. If the surface tension of the soap solution is $40 \ dyne/cm$,then the new radius is . . . . . . $cm$. Take $\pi = \frac{22}{7}$.

$A$ liquid drop having surface energy $E$ is sprayed into $512$ droplets of same size. The final surface energy is (in $E$)

$A$ drop of liquid of radius $R=10^{-2} \,m$ having surface tension $S=\frac{0.1}{4 \pi} \,Nm^{-1}$ divides itself into $K$ identical drops. In this process, the total change in the surface energy is $\Delta U=10^{-3} \,J$. If $K=10^\alpha$, then the value of $\alpha$ is:

The work done in blowing a soap bubble of radius $R$ is $W_1$ and that of radius $2R$ is $W_2$. The ratio of $W_1$ to $W_2$ is

Two mercury drops of radii $r$ and $2r$ merge to form a bigger drop. The surface energy released in the process is nearly (Surface tension of mercury is $S$ and take $9^{2/3} = 4.326$). (in $\pi r^2 S$)

$A$ small liquid drop of radius $R$ is divided into $27$ identical liquid drops. If the surface tension is $T$,then the work done in the process will be