If ‘T’ is the surface tension of a fluid, the energy needed to break a liquid drop of radius ’R‘ into 64 equal drops would be?

Solution:

The required energy to break the bigger droplet into 64 smaller droplets=change in surface areaX surafce tension(T)

Change in surface area= 64X4πr^2-4πR^2------------(1)

                              64X4/3πr^3=4/3πR^3

                                         =>  r=R/4

                                         =>  r^2=R^2/16-----------------(2)

Substituting value of r^2 in (1) from(2),

                                         Change in surface area= 12πR^2

So, the energy required to break the bigger droplet into 64 smaller droplets= (12πR^2)T----Ans