Question

The surface energy of a liquid drop is 'V'. It is sprayed into 1000 equal droplets. The surface energy of all the droplets is ______.

पर्याय

• V

• 10 V

• 100 V

• 1000 V

Answer 1

The surface energy of a liquid drop is 'V'. It is sprayed into 1000 equal droplets. The surface energy of all the droplets is 10 V.

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 × 1000

\[\therefore\] R³ = 1000 r³

\[\therefore\] R = 10r

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

Total surface energy of small droplets

V' = nA'T = 1000 × 4πr² × T = 1000 × 4π × (\[\frac {R}{10}\])² × T = \[\frac {1000}{100}\] × 4πR²T

\[\therefore\] V' = 10 × V