Question

Calculate the energy spent in spraying a drop of mercury of radius $R$ into $n$ droplets

all of same size. Given the surface tension of mercury is $T.$

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

Answer 1

The correct option is A $4\pi R^{2}T(n^{1/3}-1)$

$\begin{array}{cc}n\cdot \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3& \\ \Rightarrow n{r}^3=R^3& ...\left(i\right)\\ E=\left(n\cdot 4\pi r^2-4\pi R^2\right)T& \\ =4\pi T\left(n\cdot {\left(\frac{R^3}{n}\right)}^{\frac{2}{3}}-R^2\right)& \\ =4\pi T{R}^2\left(n^{1/3}-1\right)& \\ Ans.\left(A\right)& \end{array}$