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

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Solution

Q.
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 $(\frac{L_{B}}{L_{A}})$ of angular momentum ( $L_{B}$ ) of planet B to that of planet A( $L_{A}$ ) is closest to integer __________. [2025]

Ans.
(8)

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

Here M is mass of star

$\frac{L_{B}}{L_{A}} = \frac{m_{B}}{m_{A}} \sqrt{\frac{R_{B}}{R_{A}}} = 4 \sqrt{2} \sqrt{\frac{2}{1}}$

$\Rightarrow \frac{L_{B}}{L_{A}} = 8$

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