Two planets A and B of equal mass|Gravitation|JEEMAIN-2022

JEE MAIN 2022

28-06-22 S1

Question

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

Select the correct option:

$2 r_A^2=r_B^2$

$r_A^3=2 r_B^3$

$r_A^3=3 r_B^3$

$\mathrm{T}_{\mathrm{A}}^2-\mathrm{T}_{\mathrm{B}}^2=\frac{\pi^2}{\mathrm{GM}}\left(\mathrm{r}_{\mathrm{B}}^3-4 \mathrm{r}_{\mathrm{A}}^3\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution