Electrostatics

JEE Main level, numerical answer, medium

193 of 311

Question 193 of 311

512512 identical drops of mercury are charged to a potential of 2V2V each. The drops are joined to form a single drop. The potential of this drop is VV in Volt.

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Answer: 128

Q=512qQ=512q
Volumei=VolumefVolume{}_{i}=Volume{}_{f}
512×43πr3=43πR3512\times \dfrac{4}{3}\pi {r}^{3}=\dfrac{4}{3}\pi {R}^{3}
29r3=R3{2}^{9}{r}^{3}={R}^{3}
R=8rR=8r
2=kqr2=\dfrac{kq}{r}
V=kQR=k512q8rV=\dfrac{kQ}{R}=\dfrac{k512q}{8r}
V=128VV=128V.

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