First slide

Surface tension and surface energy

Question

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

Moderate

A

1000 : 1
B

1 : 1000
C

10 : 1
D

1 : 10

Solution

As volume remain constant therefore $R = n^{1 / 3} r$
$\frac{surface energy of one big drop}{surface energy of n drop} = \frac{4 {πR}^{2} T}{n \times 4 {πr}^{2} T}$
$\frac{R^{2}}{{nr}^{2}} = \frac{n^{2 / 3} r^{2}}{{nr}^{2}} = \frac{1}{n^{1 / 3}} = \frac{1}{(1000)^{1 / 3}} = \frac{1}{10}$

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