Two planets, A and B are orbiting a common star in circular orbits of radii R A and R B , respectively, with R B =2 R A . The planet B is 4 √(2) times more massive than planet A. The ratio (frac L B L A ) of angular momentum ( L B ) of planet B to that of planet A ( L A ) is closest to integer

Physics · Gravitation

JEE Main 2025 — 29 January, Evening Shift — Question 40

Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_{A}$ and $R_{B}$ , respectively, with $R_{B}=2 R_{A}$ . The planet $B$ is $4 \sqrt{2}$ times more massive than planet A. The ratio $\left(\frac{L_{B}}{L_{A}}\right)$ of angular momentum $\left(\mathrm{L}_{\mathrm{B}}\right)$ of planet B to that of planet $\mathrm{A}\left(\mathrm{L}_{\mathrm{A}}\right)$ is closest to integer $\qquad$

Answer: 8

Numerical answer — enter this value.

Step-by-step solution

$L=m v_{0} R=m \sqrt{\frac{G M}{R}} R=m \sqrt{G M R}$

here M is mass of star

$\frac{L_{B}}{L_{A}}=\frac{m_{B}}{m_{A}} \sqrt{\frac{\mathrm{R}_{B}}{\mathrm{R}_{A}}}$

$=4 \sqrt{2} \sqrt{\frac{2}{1}}$

$\frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{L}_{\mathrm{A}}}=8$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Evening Shift
Subject: Physics
Chapter: Gravitation
Topic: Planetary Motion & Binary Star System (Kepler's Law)