Gravitation

A planet of mass

*M*, has two natural satellites with masses*m*_{1}and*m*_{2}. The radii of their circular orbits are*R*_{1}and*R*_{2}respectively. Ignore the gravitational force between the satellites. Define*v*_{1},*L*_{1},*K*_{1}and*T*_{1}to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and*v*_{2},*L*_{2},*K*_{2}and*T*_{2}to be the corresponding quantities of satellite 2. Given*m*_{1}/*m*_{2}= 2 and*R*_{1}/*R*_{2}= 1/4, match the ratios in List-I to the numbers in List-II.LIST–I |
LIST–II |
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P. |
$\frac{{v}_{1}}{{v}_{2}}$ | 1. |
$\frac{1}{8}$ |

Q. |
$\frac{{L}_{1}}{{L}_{2}}$ | 2. |
1 |

R. |
$\frac{{K}_{1}}{{K}_{2}}$ | 3. |
2 |

S. |
$\frac{{T}_{1}}{{T}_{2}}$ | 4. |
8 |

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JEE Advanced 2018