Question

A spherical liquid drop of radius 7 cm is divided to 27 equal droplets if the surface tension i

Answer 1

your question is -> A spherical liquid drop of diameter 7cm is divided into 27 droplets of equal size.calculate the resultant change in the energy.the surface tension of the liquid is 2 × 10^-3 N/m

solution : A liquid drop breaks into 27 droplets of equal size .

Means , volume of big drop = 27 × volume of each droplet

Let R is the radius of big drop and r is the radius of small droplet.

4/3πR³ = 27 × 4/3 πr³

R³ = (3r)³ ⇒ R = 3r

intial energy of liquid drop = E₁ = T.A { here T is surface tension and A is area}

E₁ = T × 4πR²

final energy of 27 droplets = E₂= 27T.a {T is surface tension and a is area}

E₂= 27T × 4πr²

Now, change in energy = E₂ - E₁

= 27T × 4πr² - T × 4πR²

= T × 4π [ 27r² - R² ]

= T × 4π [ 27(R/3)² - R² ] { ∵R = 3r }

= T × 4π [ 3R² - R²]

= T × 4π × 2R²

= 8πR²T

now, putting value of R = 7cm = 0.07m and T = 2 × 10^-3 N/m

so, change in energy = 8 × 3.14 × (0.07)² × 2 × 10^-3 J

= 2.46 × 10-⁴ J