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/(sqrt(3))`

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))=(GMm)/(r_(A)^(2))`
`F_(B)=(GMm)/(r_(B)^(2))`
`(F_(B))/(F_(A))=(R_(A)^(2))/(r_(B)^(2))=1/9`