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_(1)^(2))/(r_(2)^(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) gt R`
D. `(F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1) lt R` and `r_(2) lt R`

Answer

A

Explanation

Solid sphere :

Gravitational field:
`rleR,E=(GMr)/(R^(3)) implies E prop r`
`rgeR,E=(GM)/(r^(2)) implies E prop 1//r^(2)`
`F=mE implies F prop E`