Question

The work done to split a liquid drop of radius R into N identical drops is (take $\sigma$ as the surface tension of the liquid):

• A. $4\pi R^2(N^{1/3}-1)\sigma$
• B. $4\pi R^{2}N\sigma$
• C. $4\pi R^2(N^{1/2}-1)$
• D. None of these

Answer 1

Answer: (A)

$4\pi R^2(N^{1/3}-1)\sigma$

Let say radius of the each drop after splitting is $r$. Since volume of water remains same after splitting, we have

$\frac{4}{3}\pi R^3=N\times \frac{4}{3}\pi r^3\Rightarrow r=N^{-\frac{1}{3}}R$

Work done in splitting $=\Delta A\times \sigma =[N\left(4\pi {\left(N^{-\frac{1}{3}}R\right)}^2\right)-4\pi R^2]\sigma =[4\pi R^2{N}^{1/3}-4\pi R^2]\sigma =4\pi R^2(N^{1/3}-1)\sigma$