Work done in increasing the size of a soap bubble from a radius of $3 \ cm$ to $5 \ cm$ is nearly (Surface tension of soap solution $= 0.03 \ Nm^{-1}$) (in $\pi \ mJ$)

$A$ 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:

What is the ratio of the surface energy of $1$ small drop to $1$ large drop,if $1000$ small drops combine to form $1$ large drop?

The radius of a soap bubble is $r$, and the surface tension of the soap solution is $T$. Without increasing the temperature, how much energy is required to double its radius (in $\pi r^2 T$)?

The surface energy of a liquid film on a ring of area $0.15\;m^2$ is ....... $J$ (Surface tension of the liquid $= 5\;N/m$).

The surface tension of a liquid is $5 \, N/m$. If a thin film of the area $0.02 \, m^2$ is formed on a loop,then its surface energy will be