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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 90The volume of spheres.27×43πr3=43πR3where, r and R are the volume of smaller and bigger sphere respectively.⇒R=3rNow, initial potential of smaller sphere,V1=14πϵ0Qr∴Q=V1r×4πϵ0∴ Charge on 27 spheres, we haveQT=27×10×r×4πϵ0Now, charge on bigger sphereQB=V2R×4πϵ0Now, QT=QB⇒270×r×4πϵ0=V2R×4πϵ0⇒270r=V2×3r⇒V2=90 V.

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