First slide

Surface tension

Question

A liquid drop of radius R is broken into 1000 drops each of radius r. If T is surface tension, change in surface energy is

Moderate

A

$4 {πR}^{2} T$
B

$72 {πR}^{2} T$
C

$16 {πR}^{2} T$
D

$36 {πR}^{2} T$

Solution

Since, volume remains constant
$\frac{4}{3} {πR}^{3} = 1000 \times \frac{4}{3} {πr}^{3}$
[No. of small drops = 1000]
= $\frac{R}{10}$
Change in surface energy
= Increase in surface area $\times$ Surface tension
= (1000 $\times$ 4 $π$ $r^{2} - 4 {πR}^{2}) \times T$
= $4 π (1000 \times \frac{R^{2}}{100} - R^{2}) \times T = 36 {πR}^{6} T$

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