A) \[\sqrt{\frac{Gm}{4R}}\]
B) \[\sqrt{\frac{Gm}{3R}}\]
C) \[\sqrt{\frac{Gm}{2R}}\]
D) \[\sqrt{\frac{Gm}{R}}\]
Correct Answer: A
Solution :
[a] Here, centripetal force will be given by the gravitational force between the two particles. \[\frac{G{{m}^{2}}}{{{(2R)}^{2}}}=m{{\omega }^{2}}R\] \[\Rightarrow \frac{Gm}{4{{R}^{3}}}={{\omega }^{2}}\Rightarrow \omega =\sqrt{\frac{GM}{4{{R}^{3}}}}\] If the velocity of the two particles with respect to the centre of gravity is v then \[v=\sqrt{\frac{Gm}{4{{R}^{3}}}}\times R=\sqrt{\frac{GM}{4R}}\]You need to login to perform this action.
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