Q 11-09-077JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
A big drop is formed by coalescing 1000 small identical drops of water. If $E_1$ is the total surface energy of the 1000 small drops and $E_2$ is the surface energy of the single big drop, then $E_1 : E_2$ is $x : 1$, where $x = $ ______.
Numerical value type. Enter your answer.
Answer: 10
Volume is conserved: $\tfrac43\pi R^3 = 1000\times\tfrac43\pi r^3 \Rightarrow R = 10r$.
$$\frac{E_1}{E_2} = \frac{1000\times4\pi r^2}{4\pi R^2} = \frac{1000r^2}{100r^2} = 10$$
Solution by Sreeraj P, M.Sc Physics