A) \[\sqrt{2}gR\]
B) \[\sqrt{gR}\]
C) \[\frac{gR}{\sqrt{2}}\]
D) \[\sqrt{3gR}\]
E) \[\frac{\sqrt{gR}}{3}\]
Correct Answer: B
Solution :
From work-energy theorem, \[\frac{1}{2}m{{v}^{2}}=-\,GMm\left[ \frac{1}{2R}-\frac{1}{R} \right]\] \[\Rightarrow \] \[\frac{1}{2}m{{v}^{2}}=\frac{-\,GMm}{2R}\] \[\Rightarrow \] \[v=\sqrt{gR}\] \[\left( \because g=\frac{GM}{{{R}^{2}}} \right)\]You need to login to perform this action.
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