Q 11-09-086JEE MainJEE Main 2023 (25 Jan, Shift 2)Easy
A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops (ignoring evaporation), $\dfrac{u_f}{u_i}=\left(\dfrac{10}{x}\right)$. Then value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 1
Volume is conserved: $R=10r$. Total area after: $1000\times4\pi r^2$; before: $4\pi(10r)^2=400\pi r^2$.
$\dfrac{u_f}{u_i}=\dfrac{4000\pi r^2}{400\pi r^2}=10=\dfrac{10}{1}$, so $x=1$.
Solution by Sreeraj P, M.Sc Physics