Question

Work done to get ‘n’ spherical drops of equal size from a single spherical drop of water, is proportional to ______.

Options

• `(1/n^(2//3) - 1)`

• `(1/n^(1//3) - 1)`

• n^1/3 − 1

• n^4/3 − 1

Answer 1

Work done to get ‘n’ spherical drops of equal size from a single spherical drop of water, is proportional to n^1/3 − 1.

Explanation:

Work done ∝ increase in surface energy ∝ increase in surface area.

Let original drop radius = R, small drop radius = r

Volume conserved:

`4/3 pi R^3 = n * 4/3 pi r^3`

⇒ R³ = nr³

⇒ R = n^1/3 r

Initial surface area = 4πR² = 4πn^2/3r²

Final surface area = n ⋅ 4πr² = 4πnr²n

Increase in area:

ΔA ∝ 4πr²(n − n^2/3) = 4πr² ⋅ n^2/3(n^1/3 − 1)

Thus,

Work done ∝ (n^1/3 − 1)