The energy needed for breaking a liquid drop of radius ' R ' into 216 droplets, each of radius ' r ' is ' x ' times TR ^2 . The value of ' x ' is [ T = surface tension of the liquid]

Step-by-step solution

The energy required to break a liquid drop into smaller droplets depends on the increase in surface area due to the surface tension , expressed as E = T A . Volume conservation relates the radii of the large drop and the small droplets. Initially, the volume is 4 3 R^3 , and after breaking into 216 droplets of radius r , the total volume remains unchanged: 4 3 R^3 = 216 4 3 r^3 . Simplifying, R^3 = 216r^3 , so R = 6r and r = R 6 . The initial surface area is A_ initial = 4 R^2 , while the total final surface area i