A) \[\frac{3}{2}\left( \frac{T}{r} \right)\Delta r\]
B) \[\left( \frac{T}{r} \right)\Delta r\]
C) \[\frac{3}{2}\left( \frac{{{T}^{2}}}{{{r}^{2}}} \right)\Delta r\]
D) none of these
Correct Answer: A
Solution :
According to Keplers law \[{{T}^{2}}=k{{r}^{3}}\] \[T=k{{r}^{3/2}}\] \[\frac{dT}{dr}=\frac{3}{2}\frac{k{{r}^{2}}}{T}\] \[\frac{dT}{dr}=\frac{3}{2}\left( \frac{T}{r} \right)\] \[\Rightarrow \] \[\frac{\Delta T}{\Delta r}=\frac{3}{2}\left( \frac{T}{r} \right)\] \[\Delta T=\frac{3}{2}\left( \frac{T}{r} \right)\Delta r\]
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