A) \[\frac{\text{mg}}{\text{3}\,\,\text{Ka}}\]
B) \[\frac{mg}{Ka}\]
C) \[\frac{Ka}{mg}\]
D) \[\frac{Ka}{3\,\,mg}\]
Correct Answer: A
Solution :
\[K=\frac{mg/a}{\frac{\Delta V}{V}}\] and \[V=\frac{4}{3}\pi {{r}^{3}}\] \[\therefore \frac{\Delta V}{V}=3\frac{dr}{r}\] So, \[K=\frac{mg/a}{3\frac{dr}{r}}\Rightarrow \frac{dr}{r}=\frac{mg}{3Ka}\]
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