$A$ liquid drop of diameter $2 \text{ mm}$ breaks into $512$ droplets. The change in surface energy is $\alpha \times 10^{-6} \text{ J}$. The value of $\alpha$ is . . . . . . . (Take surface tension of liquid = $0.08 \text{ N/m}$)

The potential energy of a molecule on the surface of a liquid compared to the molecules inside the liquid is:

The work done in blowing a soap bubble of volume $V$ is $W$. The work required to blow a soap bubble of volume $2V$ is [where $T$ is the surface tension of the soap solution].

The surface tension of soap solution is $0.03 \,N/m$. The work done in blowing to form a soap bubble of surface area $40 \,cm^2$ (in $J$) is:

If $450 \text{ erg}$ of work is done in blowing a soap bubble of radius $r$, the additional work required to be done to blow it to a radius equal to $3r$ is (in $\text{ erg}$)

$A$ spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops (ignoring evaporation),and $\frac{u_f}{u_i} = \left(\frac{10}{x}\right)$,then the value of $x$ is $......$