The magnitudes of the gravitational field at distances `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) gt 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

when `r le R,(F_(1))/(F_(2))=(GMr_(1)//R^(3))/(GMr_(2)//R^(3))=(r_(1))/(r_(2))`
when `r gt R, (F_(1))/(F_(2))=(GM//r_(1)^(2))/(GM//r_(2)^(2))=(r_(2)^(2))/(r_(1)^(2))`