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JEE Main 2023 (25 Jan, Shift 2) · Splitting & Merging of Drops

Splitting & Merging of Drops question from JEE Main 2023 (25 Jan, Shift 2)

Q38JEE Main 2023 · 25 JAN · SHIFT 2Medium

Splitting & Merging of Drops

A spherical drop of liquid splits into 1000 identical spherical drops. If u ${}_{i}$ is the surface energy of the original drop and u ${}_{f}$ is the total surface energy of the resulting drops, then (ignoring evaporation), $\frac{u_f}{u_i} = \left(\frac{10}{x}\right)$ . Then value of x is ____________:

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

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Answer: 1

$1000\, r^3 = R^3 \Rightarrow r = R/10$ .
$u_f = 1000 \cdot 4\pi \frac{R^2}{100} T = 10\, u_i$
$\frac{u_f}{u_i} = 10 = \frac{10}{x}$
So $x = 1$ .

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