Splitting & Merging of Drops question from JEE Main 2013

Answer: (d)

1. Let radius shrink by $dr$. Surface energy released $= T \cdot d(4\pi r^2) = 8\pi r T\, dr$.
2. Heat needed to evaporate that shell $= (4\pi r^2 dr)\rho L$.
3. Condition: $8\pi r T\, dr \ge 4\pi r^2 \rho L\, dr \Rightarrow r \le \frac{2T}{\rho L}$
4. The limiting radius is $\frac{2T}{\rho L}$, so the answer is (d).