Question

A spherical drop of liquid splits into 1000 identical spherical drops If $u _{ i }$ is the surfice energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation), $\frac{u_f}{u_i}=\left(\frac{10}{x}\right)$ Then value of $x$ is ___

Answer 1

The correct answer is 1.
Surface Tension =T
R : Radius of bigger drop
r : Radius of smaller drop
Volume will remain same

$\frac4{3} \pi R^3 = 1000 \times \frac4{3} \pi r^3$

$R= 10r$

$u_i ​ =T⋅4πR^ 2$

$\frac{u_f}{ u_i }​ ​ = \frac{1000r^2}{R^2}$

$\frac{u_f}{ u_i }​ ​ = \frac{10}1$