Question

What change in surface energy will be noticed when a drop of radius $R$ splits up into $1000$ droplets of radius $r$, surface tension $T ?$

• A. $4 \,\pi R^{2} T$
• B. $7\, \pi R^{2} T$
• C. $16 \,\pi R^{2} T$
• D. $36\, \pi R^{2} T$

Answer 1

Answer: (D)

Increase in surface energy $=$ surface tension $\times$ increase in surface area
$=S\left(1000 \times 4 \pi r^{2}-4 \pi R^{2}\right)$
$(100 \times \frac{4}{3} \pi r^{3}=\frac{4}{3} R^{2} $ or $r=\frac{R}{10}) $
$=S \times 4 \pi\left(1000 \times \frac{R^{2}}{100}-R^{2}\right)=36 \,\pi R^{2} S$