Question

A liquid drop having surface energy E is spread into 729 droplets of same size. The final surface aenergy of the droplets is ______.

Options

• 6 E

• 9 E

• E

• 3 E

Answer 1

A liquid drop having surface energy E is spread into 729 droplets of same size. The final surface aenergy of the droplets is 9 E.

Explanation:

Let R be radius of bigger drop and r be radius of smaller droplet.

As mass of liquid is conserved before and after spreading of drop,

\[\therefore\] mass of big drop = n × mass of droplet

ρ × \[\frac {4}{3}\]πR³ = ρ × \[\frac {4}{3}\]πr³ × 729

\[\therefore\] R³ = 729 r³

\[\therefore\] R = 9r

Surface energy of bigger drop = E = AT = (4πR²)T

Total surface energy of small droplets E' = nA'T = 729 × 4πr² × T

= 729 × 4π × \[\left(\frac{\mathrm{R}}{9}\right)^2\] × T = \[\frac {729}{81}\] × 4πR²T

\[\therefore\] E' = 9 × E