A) \[\sqrt{\frac{GM}{8{{R}^{3}}}}\]
B) \[\sqrt{\frac{GM}{2{{R}^{3}}}}\]
C) \[\sqrt{\frac{GM}{4{{R}^{3}}}}\]
D) \[\sqrt{\frac{3\sqrt{3}GM}{8{{R}^{3}}}}\]
Correct Answer: A
Solution :
[a] In \[\Delta AOB: cos 60{}^\circ = R\Rightarrow OB = 2R\] Here gravitational force will provide the required centripetal force. Hence. \[\frac{GMm}{{{\left( OB \right)}^{2}}}=m\left( OB \right){{\omega }^{2}}\] \[\Rightarrow \omega =\sqrt{\frac{GM}{{{(OB)}^{3}}}}=\sqrt{\frac{GM}{{{(2R)}^{3}}}}\Rightarrow \omega =\sqrt{\frac{GM}{8{{R}^{3}}}}\]You need to login to perform this action.
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