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Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

Asked in NEET 2021 · Coalescing charged drops

(1) 660 V
(2) 1320 V
(3) 1520 V
(4) 1980 V

Answer: (4) 1980 V

Step-by-step solution

Volume is conserved: 27×4/3π r³=4/3π R³, so R=3r.

Charge is conserved: Q=27q.

V=(kQ)/R=(27)/3·(kq)/r=9×220=1980 V.

Why the other options are wrong

(1) Scales the potential by n^1/3=3, the growth in radius, forgetting that the charge grows 27 times: V∝Q/R goes up by n^2/3=9.
(2) No single slip gives 1320 V; it is 6 times 220 V, and the factor is 27^2/3=9.
(3) No single slip gives 1520 V; it is not a whole multiple of 220 V, and the factor is 27^2/3=9.

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