Q 12-02-139JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
$27$ similar drops of mercury are maintained at $10$ V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ______ times that of a smaller drop.
Numerical value type. Enter your answer.
Answer: 243
Volume is conserved: $R^3 = 27r^3 \Rightarrow R = 3r$. Charge: $Q = 27q$.
Electrostatic energy of a charged sphere $U = \dfrac{kQ^2}{2R}$:
$$\frac{U_{big}}{U_{small}} = \frac{(27)^2}{3} = 243$$
Solution by Sreeraj P, M.Sc Physics