A) \[8000\text{ }m/s\]
B) \[\frac{8000}{\sqrt{2}}\text{ }m/s\]
C) \[\text{8000}\sqrt{2}\text{ }m/s\]
D) None of these
Correct Answer: B
Solution :
[b] Conserving angular momentum \[m({{V}_{1}}\cos 60{}^\circ ).4R=m{{V}_{2}}R\] \[\frac{{{V}_{2}}}{{{V}_{1}}}=2\] Conserving energy of the system, we get \[-\frac{GMm}{4R}+\frac{1}{2}mV_{1}^{2}=-\frac{GMm}{R}+\frac{1}{2}mV_{2}^{2}\] \[\frac{1}{2}V_{2}^{2}-\frac{1}{2}V_{1}^{2}=\frac{3}{4}\frac{GM}{R}\] or \[V_{1}^{2}=\frac{1}{2}\frac{GM}{R}\] \[\Rightarrow \,\,\,{{V}_{1}}=\frac{1}{\sqrt{2}}\sqrt{64\times {{10}^{6}}}=\frac{8000}{\sqrt{2}}m/s\]You need to login to perform this action.
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