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JEE Physics Practice Question

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

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