A) \[\sqrt[2]{\frac{G}{a}({{M}_{1}}+{{M}_{2}})}\]
B) \[\sqrt[2]{\frac{2G}{a}({{M}_{1}}+{{M}_{2}})}\]
C) \[\sqrt[2]{\frac{Gm}{a}({{M}_{1}}+{{M}_{2}})}\]
D) \[\sqrt[2]{\frac{Gm({{M}_{1}}+{{M}_{2}})}{d({{R}_{1}}+{{R}_{2}})}}\]
Correct Answer: A
Solution :
Condition for escaping of a particle is \[KE=PE\] or \[\frac{1}{2}m{{v}^{2}}=\frac{G{{M}_{1}}m}{d/2}+\frac{G{{M}_{2}}m}{d/2}\] \[{{v}^{2}}=\frac{4G}{d}({{M}_{1}}+{{M}_{2}})\] \[v=2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{d}}\]You need to login to perform this action.
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