A) \[1.99\times {{10}^{30}}\,kg\]
B) \[7.56\times {{10}^{22}}\,kg\]
C) \[5.98\times {{10}^{24}}\,kg\]
D) \[7.65\times {{10}^{22}}\,kg\]
Correct Answer: D
Solution :
\[{{g}_{m}}=\frac{G{{M}_{m}}}{R_{m}^{2}}\] and \[{{g}_{m}}=\frac{{{g}_{e}}}{6}=\frac{9.8}{6}\ m/{{s}^{2}}\]\[=1.63\ m/{{s}^{2}}\] Substituting \[{{R}_{m}}=1.768\times {{10}^{6}}m,\]\[{{g}_{m}}=1.63\ m/{{s}^{2}}\] and \[G=6.67\times {{10}^{-11}}N\text{-}{{m}^{2}}/k{{g}^{2}}\] We get \[{{M}_{m}}=7.65\times {{10}^{22}}kg\]
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