Question

The energy required to split a liquid drop having surface tension $T$ and radius $R$ into $n$ identical droplets is:

• A. $8\pi R^2(n^{1/3}-1)T$
• B. $4\pi R^2(n^{1/3}-1)T$
• C. $8\pi R^2(n^{2/3}-1)T$
• D. $4\pi R^2(n^{2/3}-1)T$

Answer 1

Answer: (B)

$4\pi R^2(n^{1/3}-1)T$

Initial energy $=4\pi R^{2}T$

initial volume = final volume

$\frac{4}{3}\pi R^3=n\frac{4}{3}\pi r^3\Rightarrow r=R{\left(n\right)}^{-1/3}$
New $SE=\left(n4\pi r^2\right)T$
$=4\pi T{R}^2{n}^{1/3}$
Energy required $=4\pi T{R}^2{n}^{1/3}-4\pi R^{2}T$
$=4\pi R^2\left(n^{1/3-1}\right)T$

Hence,

Option B is correct.