Q 11-07-055JEE MainJEE Main 2025 (29 Jan, Shift 2)Easy
Two planets, A and B, are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B = 2R_A$. The planet B is $4\sqrt2$ times more massive than planet A. The ratio $\left(\dfrac{L_B}{L_A}\right)$ of the angular momentum $(L_B)$ of planet B to that of planet A $(L_A)$ is closest to integer ______.
Numerical value type. Enter your answer.
Answer: 8
For a circular orbit $v = \sqrt{GM/R}$, so $L = mvR = m\sqrt{GMR}$.
$$\frac{L_B}{L_A} = \frac{m_B}{m_A}\sqrt{\frac{R_B}{R_A}} = 4\sqrt2\times\sqrt2 = 8$$
Solution by Sreeraj P, M.Sc Physics