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 ((L_B)/(L_A)) of angular momentum

Correct answer: 0 L=mv_0 R=m GM R R=m GMR here M is mass of star aligned & L_ B ~L_ A = m_ B ~m_ A R_ B R_ A & =4 2 (2)/(1) & ~L_ B ~L_ A =8 aligned

JEE Main 202529 JanuaryEvening Shift

JEE Main 2025 · 29 January · Evening Shift · Physics · Gravitation

Two planets, A and B are orbiting a common star in circular orbits...

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

is

4 \sqrt{2}

times more massive than planet A

. The ratio

\left(\frac{L_B}{L_A}\right)

of angular momentum

\left(L_B\right)

of planet

B

to that of planet

A\left(L_A\right)

is closest to integer ________.

\mathrm{L}=\mathrm{mv}_0

\mathrm{R}=\mathrm{m}

\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}

\mathrm{R}=\mathrm{m}

\sqrt{\mathrm{GMR}}

here M is mass of star

\begin{aligned} & \frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{~L}_{\mathrm{A}}}=\frac{\mathrm{m}_{\mathrm{B}}}{\mathrm{~m}_{\mathrm{A}}} \sqrt{\frac{\mathrm{R}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{A}}}} \\ & =4 \sqrt{2} \sqrt{\frac{2}{1}} \\ & \frac{\mathrm{~L}_{\mathrm{B}}}{\mathrm{~L}_{\mathrm{A}}}=8 \end{aligned}