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

• A. $1:10$
• B. $1:15$
• C. $1:20$
• D. $1:25$

Answer 1

Answer: (C)

As volume remains constant $R^{3} = 8000 r^{3}$ $\therefore R = 20 r$
$\frac{\text{Surface energy of one big drop}}{\text{Surface energy of 8000 small drop}} = \frac{4 \pi R^{2} T}{8000 \, 4 \pi r^{2} T}$
$= \frac{R^{2}}{8000 r^{2}} = \frac{\left(\right. 20 r \left.\right)^{2}}{8000 r^{2}} = \frac{1}{20}$