A) 3, 27
B) 27, 3
C) 27, 27
D) 3, 3
Correct Answer: B
Solution :
Key Idea: In coalescing into a single drop charge remains conserved. Abo volume before and after coalescing remains same. Let R and r be the radii of bigger and each smaller drop respectively. In coalescing into a single drop, charge remains conserved. Hence, charge on bigger drop \[\text{=}\,\,\text{27}\,\text{ }\!\!\times\!\!\text{ }\,\,\text{charge}\,\text{on}\,\text{smaller}\,\text{drop}\] ie, \[\text{q }\!\!\!\!\text{ }\,\,\text{=}\,\,\text{27q}\] Now, before and after coalescing, volume remains same. That is, \[\frac{4}{3}\pi {{R}^{3}}=27\times \frac{4}{3}\pi {{r}^{3}}\] \[\therefore \] \[R=3r\] Hence, capacitance of bigger drop \[C=4\pi {{\varepsilon }_{0}}R\] \[=4\pi {{\varepsilon }_{0}}(3r)\] \[=3(4\pi {{\varepsilon }_{0}}r)\] \[=3C\]
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