Q115 / 200 · NEET 2021 · Physics

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.

A
$660 V$
B
$1320 V$
Correct answer
C
$1980 V$
D
$1520 V$

Solution

The radius of the bigger drop will be

\frac{4}{3} π R^{3} = 27 \times \frac{4}{3} π r^{3} \Rightarrow R = 3 r

, the potential of the small drop,

V = \frac{K q}{r}

. The potential of the big drop

Q = n q, V' = \frac{K Q}{R} \Rightarrow V' = \frac{K n q}{R}

As we know, $V'_{} = n^{2 / 3} V$ $= (27)^{2 / 3} \times 220$ $= 1980 V$

Hence, the correct answer is option: 'C'.

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