A) \[1.62\times {{10}^{22}}kg\]
B) \[0.72\times {{10}^{22}}kg\]
C) \[2.16\times {{10}^{26}}kg\]
D) \[1.22\times {{10}^{22}}kg\]
E) \[3.6\times {{10}^{22}}kg\]
Correct Answer: C
Solution :
Escape velocity of a planet \[=3\times \] Escape velocity of the earth \[\sqrt{\frac{2G{{M}_{p}}}{{{R}_{p}}}}=3\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\] \[\frac{{{M}_{p}}}{{{R}_{p}}}=9\frac{{{M}_{e}}}{{{R}_{e}}}\] \[\frac{{{M}_{p}}}{4{{R}_{e}}}=9\frac{{{M}_{e}}}{{{R}_{e}}}\] \[\therefore \] \[{{M}_{p}}=36{{M}_{e}}=36\times 6\times {{10}^{24}}\] \[=2.16\times {{10}^{26}}kg\]
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