A) \[\frac{g{{R}^{2}}}{R+x}\]
B) \[\frac{g{{R}^{2}}}{R-x}\]
C) \[gx\]
D) \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\]
Correct Answer: D
Solution :
[d] Gravitational force provides the necessary centripetal force. \[\therefore \frac{m{{v}^{2}}}{\left( R+x \right)}=\frac{GmM}{{{\left( R+x \right)}^{2}}}also\,\,g=\frac{GM}{{{R}^{2}}}\] \[\therefore \frac{m{{v}^{2}}}{\left( R+x \right)}=m\left( \frac{GM}{{{R}^{2}}} \right)\frac{{{R}^{2}}}{{{\left( R+x \right)}^{2}}}\frac{n!}{r!\left( n-r \right)!}\] \[\therefore \frac{m{{v}^{2}}}{\left( R+x \right)}=mg\frac{{{R}^{2}}}{{{\left( R+x \right)}^{2}}}\] \[\therefore {{v}^{2}}=\frac{g{{R}^{2}}}{R+x}\Rightarrow v={{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\]
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