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

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 =10 r $
$ u _{ i }= T \cdot 4 \pi R ^2 $
$ u _{ f }= T \cdot 4 \pi r ^2 \times 1000$
$ \frac{ u _{ f }}{ u _{ i }}=\frac{1000 r ^2}{ R ^2}$
$\frac{ u _{ f }}{ u _{ i }}=\frac{10}{1}$
$\text { So, } x =1$