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

Answer

A

Explanation

`g=4/3 pi p Gr` or `g prop r`
`g=(GM)/(r^(2))` or `g prop (1)/(r^(2))`
if `r_(1) lt R and r_(2) t R` then `(F_(1))/(F_(2))=(g_(1))/(g_(2))=(r_(1))/(r_(2))`