JEE MAIN - Physics (2022 - 28th June Morning Shift - No. 5)
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?
$$2r_A^2 = r_B^3$$
$$r_A^3 = 2r_B^3$$
$$r_A^3 = 4r_B^3$$
$$T_A^2 - T_B^2 = {{{\pi ^2}} \over {GM}}\left( {r_B^3 - 4r_A^3} \right)$$
Explanation
$${T_A} = 2{T_B}$$
Now $$T_A^2 \propto r_A^3$$
$$ \Rightarrow {\left( {{{{r_A}} \over {{r_B}}}} \right)^3} = {\left( {{{{T_A}} \over {{T_B}}}} \right)^2}$$
$$ \Rightarrow r_A^3 = 4r_B^3$$
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