Gravitation

JEE Main level, single correct, medium

16 of 223

Question 16 of 223

The planet Mars has two moons, if one of them has a period 77 hours, 3030 minutes and an orbital radius of 9.0×103km.9.0\times {10}^{3}km. Find the mass of Mars.
{\left\{\right. Given 4π2G=6×1011N−1m−2kg2}\left.\dfrac{4{\pi }^{2}}{G}=6\times {10}^{11}{N}^{-1}{m}^{-2}{kg}^{2}\right\}

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Answer: (D) 6.00×1023kg6.00\times {10}^{23}kg

Option DD is correct.
T2=4π2GM⋅r3{T}^{2}=\dfrac{4{\pi }^{2}}{GM}\cdot {r}^{3}
M=4π2G⋅r3T2M=\dfrac{4{\pi }^{2}}{G}\cdot \dfrac{{r}^{3}}{{T}^{2}}
By putting values
M=6×1023M=6\times {10}^{23}

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