A) \[\frac{1}{2}\mu F\]
B) \[\frac{1}{4}\mu F\]
C) \[\frac{1}{8}\mu F\]
D) 8 \[\mu F\]
Correct Answer: A
Solution :
Let R and r be the radii of bigger and each smaller drop respectively. \[\therefore \] \[\frac{4}{3}\pi {{R}^{3}}=8\times \frac{4}{3}\pi {{r}^{3}}\] \[\Rightarrow \] \[R=2r\] ?(1) The capacitance of a smaller spherical drop is \[C=4\pi {{\varepsilon }_{0}}r\] ...(2) The capacitance of bigger drop is \[C=4\pi {{\varepsilon }_{0}}R\] \[2\times 4\pi {{\varepsilon }_{0}}r\] \[(\because R=2r)\] \[=2C\] [from eq (2)] \[\therefore \] \[C=\frac{C}{2}\] \[=\frac{1}{2}\mu F\] \[(\because C=1\mu F)\]
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