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Question

The radius of a planet is 74×103 km. A satellite of this planet completes one revolution in 16.7 days. If the radius of the orbit of satellite is 27 times the radius of planet, then the mass of planet is

A
2.4×1026 kg
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B
2.4×1030 kg
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C
2.4×1023 kg
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D
2.4×1042 kg
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Solution

The correct option is A 2.4×1026 kg
R=74×106m
T=16.7×60×24×60sec=1.44288×106sec
r=27R=27×74×106m=1.998×109m
T=2πr3GMT24π2=r3GM
mass m=r34π2GT2=(2×109)3×4×9.866.67×1011×(1.4)2×1012
m=2.4×1027+1112kg
m=2.4×1026kg

1185322_1279036_ans_fbebc86fec5f4085a9360e186bafd43a.jpg

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