The work done in blowing a soap bubble of volume $V$ is $W$. The work done in blowing the bubble of volume $2V$ from the same soap solution is

The surface tension of a 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:

$A$ mercury drop of radius $1 \ cm$ is sprayed into $10^6$ drops of equal size. The energy expended in joules is (surface tension of mercury is $460 \times 10^{-3} \ N/m$).

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

The amount of work done to break a big water drop of radius $R$ into $27$ small drops of equal radius is $10 \ J$. The work done required to break the same big drop into $64$ small drops of equal radius will be (in $J$)

$A$ 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 $......$