A) \[\sqrt{5}\,\,{{\upsilon }_{es(e)}}\]
B) \[5\,\,{{\upsilon }_{es(e)}}\]
C) \[2\sqrt{5}\,\,{{\upsilon }_{es(e)}}\]
D) \[10\,\,{{\upsilon }_{es(e)}}\]
Correct Answer: A
Solution :
\[{{\upsilon }_{e{{s}_{(e)}}}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] \[{{\upsilon }_{e{{s}_{(p)}}}}=\sqrt{\frac{2G{{M}_{P}}}{{{R}_{P}}}}\] (Here:\[{{M}_{p}}=10\text{ }{{M}_{e}},\text{ }{{R}_{p}}=2{{R}_{e}}\]) \[{{\upsilon }_{e{{s}_{(p)}}}}=\sqrt{\frac{2G\times 10{{M}_{e}}}{2{{R}_{e}}}}\] ?.(2) From Eqs. (1) and (2), we have \[\frac{{{\upsilon }_{es(e)}}}{{{\upsilon }_{es(p)}}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\times \sqrt{\frac{2{{R}_{e}}}{2G\times 10{{M}_{e}}}}\] \[{{\upsilon }_{es(p)}}=\sqrt{5}{{\upsilon }_{es(e)}}\]
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