27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is times that of a smaller drop.

Question

Accepted Answer

243. Volume is conserved when the drops merge: 27(4/3π r³)=4/3π R³, so R=3r. Charge is conserved too: Q=27q. For a charged sphere the self energy goes as U∝(Q²)/R. (U_big)/(Uₛₘₐₗₗ)=((27q)²/(3r))/(q²/r)=(729)/3=243. (The quoted 10 V is not needed for a ratio.)

27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ______ times that of a smaller drop.

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