A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is α × 10⁻⁶ J. The value of α is _______. (Take surface tension of liquid = 0.08 N/m) (a) 10 (b) 7 (c) 8 (d) 11

Answer: (b). Use Δ E = 4π R² T(n1/3 - 1) with R = 1 mm = 10⁻³ m. n = 512 ⇒ n1/3 = 8 Δ E = 4π (10⁻⁶)(0.08)(7) = 7.04 × 10⁻⁶ J So α ≈ 7, answer (b).

A liquid drop of diameter 2 mm breaks into 512 droplets. The change… | JEE Main 2026 (2 Apr, Shift 1)

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Splitting & Merging of Drops

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______. (Take surface tension of liquid = 0.08 N/m)

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Answer: (b)

Use $\Delta E = 4\pi R^2 T\left(n^{1/3} - 1\right)$ with $R = 1\text{ mm} = 10^{-3}\text{ m}$ .
$n = 512 \Rightarrow n^{1/3} = 8$
$\Delta E = 4\pi (10^{-6})(0.08)(7) = 7.04 \times 10^{-6}\text{ J}$
So $\alpha \approx 7$ , answer (b).

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