Two satellites `A` and `B` of the same mass are revolving around the earth in the concentric circular orbits such that the distance of satellite `B` from the centre of the earth is thrice as compared to the distance of the satellite `A` from the centre of the earth. The ratio of the centripetal force acting on `B` as compared to that on `A` is

Options

A. `1/3`
B. 3
C. `1/9`
D. `(1)/(sqrt3)`

Answer

C

Explanation

`V_(A) = sqrt((GM )/(r_(A)))and V_(B) =sqrt((GM )/(r_(B)))`
Given ` r_(B) =3r_(A)`
Now `F_(A) =(mv_(A)^(2))/( r_(A))=(M)/(r_(A))(GM )/(r_(A))=(GM m)/(r_(A)^(2))`
`F_(B) =(GM m)/(r_(B)^(2))implies(F_(B))/(F_(A))=(R_(4)^(2))/(r_(B)^(2))=1/9`