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 | ||
P. | 1. | ||
Q. | 2. | 1 | |
R. | 3. | 2 | |
S. | 4. | 8 |
Text Solution
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(P) v 0 = 
= 
= 
(Q) L = mvR
= 
= 
= 
= 
x 
x 
= 1
(R) KE = 
= 
x 
= 
x 
= 8
(S) 
= 
= 
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