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Gravitation question

2022 · 28 Jun · Shift 1 · Q47
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  5. /2022 · 28 Jun · Shift 1 · Q47

Gravitation question

2022 · 28 Jun · Shift 1 · Q47

JEE MainPhysicsGravitationMCQ+4 / −1
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
  1. A
    2rA2=rB32r_A^2 = r_B^32rA2​=rB3​
  2. B
    rA3=2rB3r_A^3 = 2r_B^3rA3​=2rB3​
  3. C
    rA3=4rB3r_A^3 = 4r_B^3rA3​=4rB3​
  4. D
    TA2−TB2=π2GM(rB3−4rA3)T_A^2 - T_B^2 = {{{\pi ^2}} \over {GM}}\left( {r_B^3 - 4r_A^3} \right)TA2​−TB2​=GMπ2​(rB3​−4rA3​)
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