A) \[V{{n}^{2/3}}\]
B) \[V{{n}^{1/3}}\]
C) \[\sqrt{Vn}\]
D) \[\frac{V}{n}\]
Correct Answer: A
Solution :
Here: Number of small drops \[=n\] Charge on each drop = V volt Volume of n drops = Volume of single large drop \[n\times \frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi {{R}^{3}}\] \[R={{n}^{1/3}}r\] The potential on a small drop is \[V=\frac{q}{4\pi {{\varepsilon }_{0}}r}\] The potential on a large drop is \[=\frac{nq}{4\pi {{\varepsilon }_{0}}R}=\frac{nq}{4\pi {{\varepsilon }_{0}}({{n}^{1/3}}r)}\] \[=\frac{q}{4\pi {{\varepsilon }_{0}}}{{n}^{2/3}}=V{{n}^{2/3}}\]
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