A) \[4\sqrt{gR}\]
B) \[\sqrt{2gR}\]
C) \[\sqrt{gR}\]
D) \[\sqrt{4gR}\]
Correct Answer: B
Solution :
According to law of conservation of energy. \[\frac{1}{2}\,m{{v}^{2}}\,-\frac{GMm}{R}=\frac{1}{2}\,mv_{1}^{2}\,+0\] \[\frac{1}{2}\,mv_{1}^{2}=\frac{1}{2}\,m{{v}^{2}}-\frac{GMm}{R}\] \[v_{1}^{2}={{v}^{2}}-\frac{2GM}{R}={{v}^{2}}-v_{e}^{2}\] \[\therefore \] \[{{v}_{1}}=\sqrt{{{v}^{2}}-v_{e}^{2}}=\sqrt{4gR-2gR}=\sqrt{2gR}\]
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