The magnitude of the gravitational field at distance `r_(1)` and `r_(2)` from the centre of a uniform sphere of radius `R` and mass `M` are `F_(1)` and `F_(2)` respectively. Then:

Options

A. `(F_(1)//F_(2))=(r_(1)//r_(2))` if `r_(1) lt R` and `r_(2) lt R`
B. `(F_(1)//F_(2))=(r_(2)//r_(1))^(2)` if `r_(1) gt R` and `r_(2) gt R`
C. `(F_(1)//F_(2))=(r_(1)//r_(2))` if `r_(1) gt R` and `r_(2)glt R`
D. `(F_(1)//F_(2))=(r_(1)//r_(2))^(2)` if `r_(1) lt R` and `r_(2) lt R`

Answer

A, B

Explanation

`F prop r (r lt R)`
`F prop (1)/(r^(2)) (r gt R)`
`(F_(1))/(F_(2))=(r_(1))/(r_(2))` if `r lt R ` & `(F_(1))/(F_(2))=((r_(2))/(r_(1)))^(2)` if `r gt R`