A) \[{{r}_{1}}^{\frac{3}{2}}\]
B) \[{{r}_{2}}^{\frac{3}{2}}\]
C) \[\frac{{{({{r}_{1}}+{{r}_{2}})}^{\frac{3}{2}}}}{2}\]
D) \[\frac{{{({{r}_{1}}-{{r}_{2}})}^{\frac{3}{2}}}}{2}\]
Correct Answer: C
Solution :
According to Kepler's law, \[{{T}^{2}}\propto {{a}^{3}}\] Here, \[a=\]semi-major axis\[=\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)\] \[\therefore \] \[{{T}^{2}}\propto {{\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)}^{3}}\] \[\Rightarrow \] \[T\propto {{\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)}^{3/2}}\]You need to login to perform this action.
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