A) \[\sqrt{\frac{GM}{L}}\]
B) \[\sqrt{\frac{3GM}{2L}}\]
C) \[\sqrt{\frac{3GM}{L}}\]
D) \[\sqrt{\frac{2GM}{3L}}\]
E) \[\sqrt{\frac{GM}{3L}}\]
Correct Answer: A
Solution :
Given\[{{F}_{1}}={{F}_{2}}=F\]and\[\theta ={{60}^{o}}\] Resultant force\[=\sqrt{3}F\] \[\therefore \]Force on mass at A due to mass at B and C \[=\sqrt{3}\left( \frac{G{{M}^{2}}}{{{L}^{2}}} \right)\] Centripetal force for circumscribing the triangle in a circular orbit is provided by mutual gravitational interaction. ie, \[\frac{M{{v}^{2}}}{(L/\sqrt{3})}-=\sqrt{3}\left( \frac{G{{M}^{2}}}{{{L}^{2}}} \right)\]or \[v=\sqrt{\frac{GM}{L}}\]You need to login to perform this action.
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