Question

If t is the surface tension of a fluid then the energy needed to break a liquid drop of radius r into 64 equal drops

Answer 1

Let radius of small drop is a
volume of big drop = 64 × volume of each small drop

or, 4/3 π r³ = 64 × 4/3 π a³

or, r³ = 64a³

or, r = 4a => a = r/4

surface area of big drop = 4πr²
surface area of 64 small drops = 64 × 4πa²
= 64 × 4π (r/4)²
= 64 × 4π × r²/16
= 16πr²

change in surface area = 16πr² - 4πr² = 12πr²

now, energy = surface tension × change in surface area
= t × 12πr²
= 12πr²t