Question

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 _______.

Answer 1

Answer is: 8 

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

here M is mass of star

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

\(=4 \sqrt{2} \sqrt{\frac{2}{1}}\)

\(\frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{L}_{\mathrm{A}}}=8\)