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A planet of mass M, has two natural sate...

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.

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

Text Solution

Verified by Experts

The correct Answer is:
B
`v prop 1/sqrtr` , Hence correct answer is ‘B’ Also , `T prop r^(3//2)` , `K prop m/r`
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Knowledge Check

  • Two stars of mass m_(1) and m_(2) are parts of a binary star system. The radii of their orbits are r_(1) and r_(2) respectivey, measured from the centre of mass of the system. The magnitude of gravitational force m_(1) exerts on m_(2) is

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