Verified Solution • 2025–26 Session moderate

QJEEM22Ph92cc: JEE Main 2022 Physics - Class 11 JEEM22Ph92cc Solution: Two planets A and B of equal mass are having their period of…

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?

Multiple Choice Options

  • A 2rA2=rB32r_A^2 = r_B^3
  • B rA3=2rB3r_A^3 = 2r_B^3
  • C rA3=4rB3r_A^3 = 4r_B^3
  • D TA2−TB2=π2GM(rB3−4rA3)T_A^2 - T_B^2 = {{{\pi ^2}} \over {GM}}\left( {r_B^3 - 4r_A^3} \right)

Step-by-Step Verified Solution

TA=2TB{T_A} = 2{T_B}

Now TA2∝rA3T_A^2 \propto r_A^3

⇒(rArB)3=(TATB)2\Rightarrow {\left( {{{{r_A}} \over {{r_B}}}} \right)^3} = {\left( {{{{T_A}} \over {{T_B}}}} \right)^2}

⇒rA3=4rB3\Rightarrow r_A^3 = 4r_B^3

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