When a mercury drop of radius $R$ splits up into $1000$ droplets of radius $r$,the change in surface energy is ($\pi R^2 T$). ($T=$ surface tension of mercury).

$A$ soap bubble of radius $r$ is blown up to form a bubble of radius $2r$ under isothermal conditions. If $T$ is the surface tension of the soap solution, the energy spent in the blowing is: (in $\pi T r^2$)

$A$ big water drop is formed by the combination of $n$ small water droplets of equal radii. The ratio of the surface energy of $n$ droplets to the surface energy of the big drop is

The surface energy of a liquid drop is $U$. It splits up into $512$ equal droplets. The surface energy becomes (in $U$)

If $\sigma$ is the surface tension,the work done in breaking a big drop of radius $R$ into $n$ drops of equal radius is:

The surface tension of the soap water solution is $\frac{1}{10 \pi} \text{ N m}^{-1}$. The free energy of the surface layer of a soap bubble of diameter $5 \text{ mm}$ will be: