JEE Main 2022 · 28 Jun · Shift 1 · Physics Q35

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PhysicsSingle correct+4 / -1Question 35 of 90

Two planets A and B of equal mass are having their period of revolutions $T_A$ and $T_B$ such that $T_A=2T_B$ . These planets are revolving in the circular orbits of radii $r_A$ and $r_B$ respectively. Which out of the following would be the correct relationship of their orbits?

2r_A^2=r_B^3

r_A^3=2r_B^3

r_A^3=4r_B^3

T_A^2-T_B^2=\dfrac{\pi^2}{GM}\left(r_B^3-4r_A^3\right)

Answer and worked solution

Official answer: C

Kepler's third law. $T^2\propto r^3$ : $\dfrac{r_A^3}{r_B^3}=\dfrac{T_A^2}{T_B^2}=4$ , so $r_A^3=4r_B^3$ .

(C)

Topics:Kepler's laws

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JEE Main 2022 · 28 Jun · Shift 1, Physics question 35