A) \[{{\left( \frac{4{{\pi }^{2}}GM}{{{T}^{2}}} \right)}^{1/3}}\]
B) \[{{\left( \frac{4\pi GM}{{{R}^{2}}} \right)}^{1/3}}-R\]
C) \[{{\left( \frac{GM{{T}^{2}}}{4{{\pi }^{2}}} \right)}^{1/3}}-R\]
D) \[{{\left( \frac{GM{{T}^{2}}}{4{{\pi }^{2}}} \right)}^{1/3}}+R\]
Correct Answer: C
Solution :
\[T=2\pi \sqrt{\frac{{{r}^{3}}}{GM}}\,\Rightarrow \,{{T}^{2}}=\frac{4{{\pi }^{2}}}{GM}{{(R+h)}^{3}}\] \[\Rightarrow \,\,R+h={{\left[ \frac{GM{{T}^{2}}}{4{{\pi }^{2}}} \right]}^{1/3}}\Rightarrow \,h={{\left[ \frac{GM{{T}^{2}}}{4{{\pi }^{2}}} \right]}^{\frac{1}{3}}}-R\]
You need to login to perform this action.
You will be redirected in
3 sec
