A) \[\frac{1}{2R}\sqrt{\frac{1}{Gm}}\]
B) \[\sqrt{\frac{Gm}{2R}}\]
C) \[\frac{1}{2}\sqrt{\frac{Gm}{R}}\]
D) \[\sqrt{\frac{4\,Gm}{R}}\]
Correct Answer: C
Solution :
We know that the centrifugal force \[=\frac{m{{v}^{2}}}{R}\]and gravitational force\[=G\times \frac{m\times m}{4{{R}^{2}}}.\] Equating these two force\[\frac{m{{v}^{2}}}{R}\] \[=G\times \frac{m\times m}{4{{R}^{2}}}\]or\[v=\sqrt{\frac{GM}{4R}}=\frac{1}{2}\sqrt{\frac{GM}{R}}\]
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