A) \[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{1}{r}\frac{dv}{dr}=0\]
B) \[\frac{{{d}^{2}}v}{d{{r}^{2}}}-\frac{2}{r}\frac{dv}{dr}=0\]
C) \[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{2}{r}\frac{dv}{dr}=0\]
D) None of these
Correct Answer: C
Solution :
\[\frac{dv}{dr}=-\frac{A}{{{r}^{2}}}+0\]Þ\[\frac{{{d}^{2}}v}{d{{r}^{2}}}=\frac{2A}{{{r}^{3}}}\]Þ\[\frac{{{d}^{2}}v}{d{{r}^{2}}}=\frac{2}{r}\left( \frac{A}{{{r}^{2}}} \right)\] Þ \[\frac{{{d}^{2}}v}{d{{r}^{2}}}=\frac{2}{r}\left( -\frac{dv}{dr} \right)\]Þ\[\frac{{{d}^{2}}v}{d{{r}^{2}}}+\frac{2}{r}\frac{dv}{dr}=0\].
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