A large number of water drops, each of radius r, combine to have a… | JEE Main 2021 (26 Feb, Shift 1)

Q49JEE Main 2021 · 26 FEB · SHIFT 1Medium

Splitting & Merging of Drops

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be:

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Answer: (b)

Volume $V = n \cdot \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3$ , so $n \cdot 4\pi r^2 = \frac{3V}{r}$ and $4\pi R^2 = \frac{3V}{R}$ .
Energy released $= T\,\Delta A = 3VT\left(\frac{1}{r} - \frac{1}{R}\right)$
Heat per unit volume $= \frac{3T}{J}\left(\frac{1}{r} - \frac{1}{R}\right)$
So the answer is (b).

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