Two planets,A and B,are orbiting a common sta | vedclass

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(D) The angular momentum $L$ of a planet of mass $m$ in a circular orbit of radius $R$ around a star of mass $M$ is given by $L = mvr$.For a circular

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) The angular momentum $L$ of a planet of mass $m$ in a circular orbit of radius $R$ around a star of mass $M$ is given by $L = mvr$.For a circular orbit,the orbital velocity is $v = \sqrt{\frac{GM}{R}}$.Substituting this into the expression for angular momentum,we get $L = m \sqrt{\frac{GM}{R}} R = m \sqrt{GMR}$.Given $R_B = 2 R_A$ and $m_B = 4 \sqrt{2} m_A$.The ratio of angular momenta is $\frac{L_B}{L_A} = \frac{m_B \sqrt{GM R_B}}{m_A \sqrt{GM R_A}} = \frac{m_B}{m_A} \sqrt{\frac{R_B}{R_A}}$.Substituting the given values: $\frac{L_B}{L_A} = (4 \sqrt{2}) \sqrt{\frac{2 R_A}{R_A}} = 4 \sqrt{2} 	imes \sqrt{2} = 4 	imes 2 = 8$.Thus,the ratio is $8$.

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