Gravitation

JEE Main level, single correct, medium

185 of 223

Question 185 of 223

Two satellites AA and BB of masses 200kg200kg and 400kg400kg are revolving round the earth at height of 600km600km and 1600km1600km respectively. If TA{T}_{A} and TB{T}_{B} are the time periods of AA and BB respectively then the value of TB−TA{T}_{B}-{T}_{A} :
[ Given : radius of earth =6400km,=6400km, mass of earth =6×1024kg=6\times {10}^{24}kg ]

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Answer: (C) 1.33×103s1.33\times {10}^{3}s

⇒T=2πr3GM\Rightarrow T=2\pi \sqrt{\dfrac{{r}^{3}}{GM}}
⇒TA=2π(6400+600)×103GM\Rightarrow {T}_{A}=2\pi \sqrt{\dfrac{\left(6400+600\right)\times {10}^{3}}{GM}}
⇒TB=2π×10983GM\Rightarrow {T}_{B}=2\pi \times {10}^{9}\sqrt{\dfrac{{8}^{3}}{GM}}
⇒TB−TA=2π109GM[88−77]\Rightarrow {T}_{B}-{T}_{A}=\dfrac{2\pi {10}^{9}}{\sqrt{GM}}\left[8\sqrt{8}-7\sqrt{7}\right]
=314×4.107=314\times 4.107
=1289.64=1289.64
=1.289×103s=1.289\times {10}^{3}s

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