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:

Explanation

When `r_(1) gt R`, the point lies outside the sphere. Then sphere can be considered to be a point mass body whose whole mass can be supposed to be concentracted at its centre. Then gravitational intensity at a point distance `r_(1)` from the centre of sphere will be,
`I_(1) = GM//r_(1)^(2)` ..(i)
When `r_(2) lt R`, the point `P` lies inside the sphere. the unit mass body placed at `P`, will experience gravitational pull due to sphere of radius `r_(2)`, whose mass is
`M' = (M xx (4)/(3) pi r_(2)^(3))/((4)/(3) pi R^(3)) = (M r_(2)^(3))/(R^(3))`
Therefore, the gravitaional intensity at `P` will be,
`I_(2) = (Gm r_(2)^(3))/(R^(3)) x (1)/(2) = (GM r_(2))/(R^(3))` ..(ii)
So `(I_(1))/(I_(2)) = (GM)/(r_(1)^(2)) xx (R^(3))/(GM r_(2)) = (R^(3))/(r_(1)^(2) r_(2))`