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) gt R` and `r_(2) lt R`
B. `(F_(1))/(F_(2)) = (r_(2)^(2))/(r_(1)^(2))` if `r_(!) gt R` and `r_(2) gt R`
C. `(F_(1))/(F_(2)) = (r_(1)^(3))/(r_(2)^(3))` if `r_(1) lt R` and `r_(2) lt R`
D. `(F_(1))/(F_(2)) =(r_(1)^(2))/(r_(2)^(2))` if `eta lt R` and `r_(2) lt R`

Answer

B

Explanation

For `vleR, F=(GMr)/(R^(3))`
`(F_(1))/(F_(2))=(r_(1))/(r_(2))` for `r_(1) gt R` and `r_(2) lt R`
For `rgeR, F=(GM)/(r^(2))`
It implies `F prop1//r^(2)`
`:. (F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2))` for `r_(1)gtR` and `r_(2)gtR`