A) \[{{v}_{1}}={{v}_{2}}\]
B) \[{{v}_{1}}>{{v}_{2}}\]
C) \[{{v}_{1}}<{{v}_{2}}\]
D) \[\frac{{{v}_{1}}}{{{r}_{1}}}=\frac{{{v}_{2}}}{{{r}_{2}}}\]
Correct Answer: B
Solution :
\[{{F}_{1}}=\frac{GMm}{r_{1}^{2}}=\frac{g{{R}^{2}}m}{r_{1}^{2}}\] \[GM=g{{R}^{2}}\] \[{{F}_{2}}=\frac{GMm}{r_{2}^{2}}=\frac{g{{R}^{2}}m}{r_{2}^{2}}\] \[\frac{g{{R}^{2}}m}{r_{1}^{2}}=\frac{mv_{1}^{2}}{{{r}_{1}}}\] \[v_{1}^{2}=\frac{g{{R}^{2}}}{{{r}_{1}}}\] \[\Rightarrow \] \[{{v}_{1}}=\sqrt{\frac{g{{R}^{2}}}{{{r}_{1}}}}\] \[{{v}_{2}}=\sqrt{\frac{g{{R}^{2}}}{{{r}_{2}}}}\frac{{{v}_{1}}}{{{v}_{2}}}\] \[=\sqrt{\frac{{{r}_{2}}}{{{r}_{1}}}}\] We can see that \[{{v}_{1}}>{{v}_{2}}\]
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