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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.

  

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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.

(1) 660 V

(2) 1320 V

(3) 1520 V

(4) 1980 V

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Correct answer: (4) 1980 V

Explanation:

\(\frac{4}{3}\pi R^3\) = 27\((\frac{4}{3}\pi r^3)\) ⇒ R = 3r   .....(1)

V = \(\frac{Kq}{r}\) ⇒ \(\frac{V_1}{V_2}\) = \((\frac{q_1}{q_2})\)\((\frac{r_2}{r_1})\)

⇒ \(\frac{220}{V_2}\) = \((\frac{q}{27q})\)\((\frac{3r}{r})\)

⇒ \(\frac{220}{V_2}\) = \(\frac{1}{9}\)

⇒ V2 = 220 x 9 = 1980 volt

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