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Q.

A Spherical drop of liquid splits into 216 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, the ratio (ignoring evaporation) $\frac{U_{f}}{U_{i}} =$

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answer is 6.

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Detailed Solution

Surface tension =T
R: Radius of bigger drop
R: Radius of smaller drop
Volume will remain same
$\begin{array}{l} \frac{4}{3} π R^{3} = 216 \times \frac{4}{3} π r^{3} \Rightarrow R = 6 r \\ μ_{i} = T .4 π R^{2} \\ μ_{f} = T .4 π r^{2} \times 216 \\ \frac{μ_{f}}{μ_{i}} = \frac{216 r^{2}}{R^{2}} = 6 \end{array}$

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