$27$ identical drops are charged at $22\, V\,\,each.$ They combine to form a bigger drop. The potential of the bigger drop will be............ $V.$
JEE MAIN 2022, Medium
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$q \rightarrow nq$
$n \frac{4}{3} \pi r ^{3}=\frac{4}{3} \pi\left( r ^{\prime}\right)^{3}$
$\Rightarrow r ^{\prime}= n ^{\frac{1}{3} r }$
$V =\frac{ kq }{ r } \propto \frac{ n }{ n ^{1 / 3}} \propto n ^{2 / 3} \propto 27^{2 / 3} \Rightarrow v ^{\prime}=9 V =9 \times 22=198$
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