JEE Main 2025 Jan 29 Shift 2, Physics Q24: Satellite, Planetary Motion And Kepler’s Law

JEE Main2025Jan 29, Shift 2Physics

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 $42$ 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 __________.

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Solution

For a circular orbit, $v = G M_{⋆} / R$ , so $L = m v R = m G M_{⋆} R$ .

Therefore $L \propto m R$ at fixed central mass, and

$\frac{L _{B}}{L _{A}} = \frac{m _{B}}{m _{A}} \frac{R _{B}}{R _{A}} = (42) \cdot 2 = 4 \cdot 2 = 8$ .

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JEE Main 2025 Jan 29 Shift 2, Physics Q24: Satellite, Planetary Motion And Kepler’s Law

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