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Eight oil drops of same size are charged to a potential of 50 V each. These oil drops are merged into one single large drop. the The potential of the large drop in volt is

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50 V

100 V

200 V

400 V

answer is C.

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Detailed Solution

$8 \times V o l u m e o f s m a l l d r o p = V o l u m e o f b i g d r o p$

$8 (\frac{4}{3} {πr}^{3}) = \frac{4}{3} {πR}^{3}, R = 2 r, Q = 8 q$

Further, $V = \frac{1}{4 {πε}_{0}} \frac{q}{r} = 50 V$

and $V' = \frac{1}{4 {πε}_{0}} \cdot \frac{Q}{R} = \frac{1}{4 {πε}_{0}} \cdot \frac{8 q}{2 r} = 4 \times 50 = 200 V$

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