First slide

Surface tension and surface energy

Question

8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

Moderate

A

1 : 10
B

1 : 15
C

1 : 20
D

1 : 25

Solution

As volume remains constant $R^{3} = 8000 r^{3} ∴ R = 20 r$
$\begin{array}{l} \frac{Surface energy of one big drop}{Surface energy of 8000 small drop} = \frac{4 {πR}^{2} T}{8000 (4 {πr}^{2} T)} \\ = \frac{R^{2}}{8000 r^{2}} = \frac{(20 r)^{2}}{8000 r^{2}} = \frac{1}{20} \end{array}$

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