Question

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

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

Answer 1

The correct option is C 1:20

Given,

$n=8000$

If the number of small liquid drops combine to form a big drop, the mass of liquid and hence the volume of the liquid remains constant.

$\frac{4}{3}\pi R^3=n\left(\frac{4}{3}\pi r^3\right)$

$R^3=8000r^3$

$R=20r$

The surface energy of big drop,

$S=4\pi R^{2}T$ where, $T=$ surface tension

Surface energy of small 8000 drop

$s=8000\left(4\pi r^{2}T\right)$

Ratio, $\frac{S}{s}=\frac{4\pi R^{2}T}{8000\left(4\pi r^{2}T\right)}=\frac{R^2}{8000r^2}$

$\frac{S}{s}=\frac{(20r{)}^2}{8000r^2}$

$\frac{S}{s}=\frac{400r^2}{8000r^2}=\frac{1}{20}$

$S:s=1:20$

The correct option is C.