Two planets, A and B are orbiting a common star in circular orbits of radii RA and RB, respectively, with RB = 2RA. The planet B is 4√(2) times more massive than planet A. The ratio ((LB)/(LA)) of angular momentum (LB) of planet B to that of planet A (LA) is closest to integer ________. Numerical answer type. Work it out, then open the answer.

Answer: 8. L = m√(GMR), so L ∝ m√(R). (LB)/(LA) = (mB)/(mA)√((RB)/(RA)) = 4√(2)×√(2) (LB)/(LA) = 8 Answer: 8

Two planets, A and B are orbiting a common star in circular orbits of… | JEE Main 2025 (29 Jan, Shift 2)

Q15JEE Main 2025 · 29 JAN · SHIFT 2Medium

Satellites - Orbital Velocity & Period

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 $4\sqrt{2}$ times more massive than planet $A$ . The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum $(L_B)$ of planet $B$ to that of planet $A\,(L_A)$ is closest to integer ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 8

$L = m\sqrt{GMR}$ , so $L \propto m\sqrt{R}$ .
$\frac{L_B}{L_A} = \frac{m_B}{m_A}\sqrt{\frac{R_B}{R_A}} = 4\sqrt{2}\times\sqrt{2}$
$\frac{L_B}{L_A} = 8$
Answer: 8

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