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

Answer: 1

Surface Tension $=T$
$R$ : Radius of bigger drop
$r$ : Radius of smaller drop
Volume will remain same
$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\pi r^3$
$R=10r$
$u_i=T\cdot 4\pi R^2$
$u_f=T\cdot 4\pi r^2\times 1000$
$\frac{u_f}{u_i}=\frac{1000r^2}{R^2}$
$\frac{u_f}{u_i}=\frac{10}{1}$
$\text{ So, }x=1$