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Question

27 identical drops of mercury are charged simultaneously with the same potential of 10 V. Assuming the drop to the spherical, if all the charged drops are made to combine to form one large drop, then its potential will be _____ V.

A
40
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B
90
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C
160
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D
10
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Solution

The correct option is B 90
The volume of spheres.
27×43πr3=43πR3
where, r and R are the volume of smaller and bigger sphere respectively.
R=3r
Now, initial potential of smaller sphere,
V1=14πϵ0Qr
Q=V1r×4πϵ0
Charge on 27 spheres, we have
QT=27×10×r×4πϵ0
Now, charge on bigger sphere
QB=V2R×4πϵ0
Now, QT=QB
270×r×4πϵ0=V2R×4πϵ0
270r=V2×3rV2=90 V.

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