Question

One thousand small water droplets of equal size combine to form a big drop. The ratio of the final surface energy to the initial surface energy is: (Surface tension of water = 70 dyne/cm)

• A. 10:1
• B. 1000:1
• C. 1:10
• D. 1:1000

Answer 1

The correct option is C 1:10

Let the radius of smaller radius be $r$ and bigger be $R$.

Since volume remains constant, thus $\frac{4\pi R^3}{3}=1000\times \frac{4\pi r^3}{3}$

We get $R=10r$

Ratio of final surface energy to initial is

$\frac{W_f}{W_i}=\frac{T\times 4\pi R^2}{T\times 1000\times 4\pi r^2}$

$\frac{W_f}{W_i}=\frac{(10r{)}^2}{1000r^2}=1:10$