A planet of mass M, has two natural satellites with masses m1 and m2. 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 he 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.

Options

A. P - 4, Q - 2, R - 1, S - 3
B. P - 3, Q - 2, R - 4, S - 1
C. P - 2, Q - 3, R - 1, S - 4
D. P - 2, Q - 3, R - 4, S - 1

Answer

B

Explanation

`P rarr v_(0) = sqrt((GM)/(R ))`
`(v_(1))/(v_(2)) = sqrt((R_(2))/(R_(1))) = (2)/(1)`
`Q rarr L = m v R`
`(L_(1))/(L_(2)) = (m_(1))/(m_(2)) xx (v_(1))/(v_(2)) xx (R_(1))/(R_(2)) = (2)/(1) xx (2)/(1) xx (1)/(4) = 1`
`R rarr K.E. = (GMm)/(R )`
`(K_(1))/(K_(2)) = (m_(1))/(m_(2)) xx (R_(2))/(R_(1)) = (2)/(1) xx (4)/(1) = 8`
`S rarr (T_(1))/(T_(2)) = ((R_(1))/(R_(2)))^((3)/(2)) = (1)/(8)`