Question

A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be ______.

Options

• 2 πR²T

• 3 πR²T

• 4 πR²T

• 2 πRT²

Answer 1

A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be 4 πR²T.

Explanation:

Let's say that r represents the bubble's eight-sided radius. Water volume remains constant, so we have

`4/3pi"R"^3=8xx4/3pi"r"^3`

⇒ r = `"R"/2`

So the work done in this process will be = change in the surface energy i.e.

(8 × 4πr² × T) - (4πR² × T)

= `(8xx4pi("R"/2)^2xx"T")-(4pi"R"^2xx"T")`           ∵ r =`"R"/2`

= 8πR²T - 4πR²T = 4πR²T