A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be

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Solution

Q.
A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be [2024]

1 $4 {πR}^{2} T$

2 $8 {πR}^{2} T$

3 $3 {πR}^{2} T$

4 $1 / 8 {πR}^{2} T$

Ans.
(2)

Volume of liquid of drops should be constant,

   $\frac{4}{3} {πR}^{3} = 27 \times \frac{4}{3} \times {πr}^{3}$

   $R^{3} = 27 r^{3} \Rightarrow R = 3 r$

   $r = \frac{R}{3} \Rightarrow r^{2} = \frac{R^{2}}{9}$

Work done = $T \cdot ∆ A$

$= 27 T (4 {πr}^{2}) - T 4 {πR}^{2}$

   $= 27 T 4 π \frac{R^{2}}{9} - 4 {πR}^{2} T = 8 {πR}^{2} T$

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