Question

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

(1) 100 times 

(2) 10 times

(3) \(\frac {1}{100} th\)

(4) \(\frac {1}{10}th\)

Answer 1

(4) \(\frac {1}{10}th\)

Lets say radius of small droplets is r and that of big drop is R

\(\frac {4}{3} \pi R^3 = 1000 \frac {4}{3} \pi r^3\)

R = 10r

\(U _i = 1000 (4 \pi r^2S)\)

\(U_f = 4\pi R^2S\)

\(=100 (4 \pi r ^2S)\)

\(U_f = \frac {1}{10 }U_i\)