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. \[\Rightarrow \] \[\frac{4}{3}\pi \,{{R}^{3}}=8\times \frac{4}{3}\pi {{r}^{3}}\] \[\Rightarrow \] \[R=2r\] ... (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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