Electrostatic Potential Energy question from MHT CET 2026 (14 May, Shift 2)

Answer: (d)

1. Electrostatic force per unit area on a charged surface: $P = \frac{\sigma^2}{2\varepsilon_0}$, so $P \propto \sigma^2$.
2. Volume conserved: $27r^3 = R^3 \Rightarrow r = \frac{R}{3}$. Charge conserved: each small bubble has $\frac{Q}{27}$.
3. $\sigma_{small} = \frac{Q/27}{4\pi R^2/9} = \frac{1}{3}\sigma_{big}$
4. $\frac{P_{big}}{P_{small}} = 9$, answer (d) $9/1$.