A) 2600 km
B) 1600 km
C) 1400 km
D) 2000 km
Correct Answer: A
Solution :
[a] As we know, gravitational potential (v) and acceleration due to gravity (g) with height \[\operatorname{V}=\frac{-GM}{R+H}=5.4\times 1{{0}^{7}}\] ?(i) And \[g=\frac{GM}{\left( R+H \right)}=6\] ...(ii) Dividing (i) by (ii) \[\frac{\frac{-GM}{R+H}}{\frac{GM}{{{\left( R+H \right)}^{2}}}}=\frac{-5.4\times 1{{0}^{7}}}{6}\Rightarrow \frac{5.4\times {{10}^{7}}}{\left( \operatorname{R}+H \right)}=6\] \[\Rightarrow \operatorname{R}+h=9000km\,so,h=2600k\]
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