Electric Potential & Equipotentials question from JEE Main 2021 (25 Feb, Shift 1)

Answer: 128

1. Charge is conserved: $Q = nq$; volume is conserved: $\frac{4}{3}\pi R^3 = n\cdot\frac{4}{3}\pi r^3 \Rightarrow R = n^{1/3}r$
2. $V' = \frac{kQ}{R} = \frac{knq}{n^{1/3}r} = n^{2/3}V$
3. $V' = 512^{2/3}\times 2 = 64 \times 2 = 128\text{ V}$
4. So the answer is 128 V.