A) \[{{\left( \frac{GM}{R} \right)}^{1/2}}\]
B) \[{{\left( \frac{GM}{2R} \right)}^{1/2}}\]
C) \[{{\left( \frac{2GM}{R} \right)}^{1/2}}\]
D) \[{{\left( \frac{4GM}{R} \right)}^{1/2}}\]
Correct Answer: A
Solution :
From conservation of energy \[\frac{1}{2}m{{u}^{2}}-\frac{GMm}{R}=\frac{1}{2}m\times {{(0)}^{2}}-\frac{GMm}{R+R}\] \[\Rightarrow \]\[{{u}^{2}}=\frac{2GM}{R}-\frac{2GM}{2R}=\frac{GM}{R}\] \[\Rightarrow \]\[u=\sqrt{\frac{GM}{R}}\]
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