Question

$8000$ identical water drops combine together 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

The correct option is C $1:20$

$n=8000$
initial radius $=r$
final radius $=R$
by equating volume we get
$(8000{)}^{\frac{1}{3}}r=R$
$20r=R$
$\frac{SE{-}_f}{SE{-}_i}=\frac{4\pi R^{2}T}{8000\times 4\pi r^{2}T}=\frac{(20r{)}^2}{8000\times r^2}$
$=\frac{1}{20}$