216 charged droplets, each of radius r and charge q, are combined to form a big drop. The ratio of potential of the big drop to the small droplet will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36
The potential of a charged spherical drop is \( V = kQ/R \). When the droplets combine, charge is conserved and the volume is conserved.
\( \displaystyle Q = 216\,q \)
\( \displaystyle \frac{4}{3}\pi R^{3} = 216 \times \frac{4}{3}\pi r^{3} \;\Rightarrow\; R = (216)^{1/3}\,r = 6r \)
\( \displaystyle \frac{V_{\text{big}}}{V_{\text{small}}} = \frac{k\,(216 q)/(6r)}{k\,q/r} = \frac{216}{6} = 36 \)
Note: The same question was also asked in CUET (UG) 2025 on 30-05-2025 (Slot 1).