A spherical drop of liquid splits into 1000 identical spherical drops. If u$_\mathrm{i}$ is the surface energy of the original drop and u$_\mathrm{f}$ is the total surface energy of the resulting drops, the (ignoring evaporation), ${{{u_f}} \over {{u_i}}} = \left( {{{10} \over x}} \right)$. Then value of x is ____________ :
Answer (integer)
1
Solution
Surface Tension $=\mathrm{T}$<br/><br/>
$\mathrm{R}$ : Radius of bigger drop<br/><br/>
$\mathrm{r}$ : Radius of smaller drop<br/><br/>
Volume will remain same<br/><br/>
$\frac{4}{3} \pi R^3=1000 \times \frac{4}{3} \pi r^3$<br/><br/>
$\mathrm{R}=10 \mathrm{r}$<br/><br/>
$\mathrm{u}_{\mathrm{i}}=\mathrm{T} \cdot 4 \pi \mathrm{R}^2$<br/><br/>
$\mathrm{u}_{\mathrm{f}}=\mathrm{T} .4 \pi \mathrm{r}^2 \times 1000$<br/><br/>
$\frac{\mathrm{u}_{\mathrm{f}}}{\mathrm{u}_{\mathrm{i}}}=\frac{1000 \mathrm{r}^2}{\mathrm{R}^2}$<br/><br/>
$\frac{\mathrm{u}_{\mathrm{f}}}{\mathrm{u}_{\mathrm{i}}}=\frac{10}{1}$<br/><br/>
So, $x=1$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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