A spherical drop of liquid splits into 1000 identical spherical drops. If is the surface energy of the original drop and is the total surface energy of the resulting drops, the (ignoring evaporation) Then value of is ___________ . [

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Solution

Q.
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, the (ignoring evaporation) $\frac{u_{f}}{u_{i}} = (\frac{10}{x}) .$ Then value of $x$ is ___________ . [2023]

Ans.
(1)

$Surface tension = T$

$R : Radius of bigger drop$

$r : Radius of smaller drop$

$Volume will remain same$

$\frac{4}{3} π R^{3} = 1000 \times \frac{4}{3} π r^{3}$ $\Rightarrow R = 10 r$

$U_{i} = T \cdot 4 π R^{2}$

$U_{f} = T \cdot 4 π r^{2} \times 1000$

$\frac{U_{f}}{U_{i}} = \frac{1000 r^{2}}{R^{2}} = \frac{10}{1}$

$So, x = 1$

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