Gravitation

JEE Main level, numerical answer, medium

201 of 223

Question 201 of 223

Two planets, AA and BB are orbiting a common star in circular orbits of radii RAR_A and RBR_B, respectively, with RB=2RAR_B=2 R_A. The planet BB is 424 \sqrt{2} times more massive than planet AA. The ratio (LBLA)\left(\frac{L_B}{L_A}\right) of angular momentum (LB)\left(L_B\right) of planet BB to that of planet A(LA)A\left(L_A\right) is closest to integer ________.

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Answer: 8

L=mv0R=mGMRR=mGMR\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
$\begin{aligned}
& \frac{\mathrm{L}_{\mathrm{B}}}{\mathrm{~L}_{\mathrm{A}}}=\frac{\mathrm{m}_{\mathrm{B}}}{\mathrm{~m}_{\mathrm{A}}} \sqrt{\frac{\mathrm{R}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{A}}}} \\
& =4 \sqrt{2} \sqrt{\frac{2}{1}} \\
& \frac{\mathrm{~L}_{\mathrm{B}}}{\mathrm{~L}_{\mathrm{A}}}=8
\end{aligned}$

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