JEE Advanced 2018 — Paper 2 — Question 15

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.