27 identical drops of mercury are charged simultaneously with the same potential of 10V. 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.
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Correct option is B)
The volume of spheres. 27×34πr3=34πR3 where, r and R are the volume of smaller and bigger sphere respectively. ⇒R=3r Now, initial potential of smaller sphere, V1=41πϵ0rQ ∴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=V2×3r⇒V2=90V.
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