A big drop is formed by coalescing 1000 small identical drops of water. If E₁ be the total surface energy of 1000 small drops of water and E₂ be the surface energy of single big drop of water, then E₁: E₂ is x: 1 where x = ________. Numerical answer type. Work it out, then open the answer.

Answer: 10. Volume conserved: 1000 r³ = R³ ⇒ R = 10r. E₁ = 1000 · 4π r² T, E₂ = 4π (10r)² T = 100 · 4π r² T E₁: E₂ = 1000: 100 = 10: 1 So x = 10.

A big drop is formed by coalescing 1000 small identical drops of… | JEE Main 2024 (30 Jan, Shift 2)

Q26JEE Main 2024 · 30 JAN · SHIFT 2Easy

Splitting & Merging of Drops

A big drop is formed by coalescing 1000 small identical drops of water. If $E_1$ be the total surface energy of 1000 small drops of water and $E_2$ be the surface energy of single big drop of water, then $E_1 : E_2$ is $x : 1$ where $x =$ ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 10

Volume conserved: $1000\, r^3 = R^3 \Rightarrow R = 10r$ .
$E_1 = 1000 \cdot 4\pi r^2 T$ , $E_2 = 4\pi (10r)^2 T = 100 \cdot 4\pi r^2 T$
$E_1 : E_2 = 1000 : 100 = 10 : 1$
So $x = 10$ .

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