The magnitude of gratitational field intensities at distance `r_(1)` and `r_(2)` from the centre of a uniform solid sphere of radius R and mass M are `I_(1)` and `I_(2)` respectively. Find the ratio of `I_(1)//I_(2)` if (a) `r_(1) gt R` and `r_(2) gt R` and (b) `r_(1) lt R` and `r_(2) lt R` (c ) `r_(1) gt R` and `r_(2) lt R`.

Explanation

Gravitational field intensity for a uniform spherical distribution of mass is given by :
`I = (GM)/(r^(2))` for `r gt R` and
`= (GM)/(R^(3))r` for `r lt R`.
(a) `r_(1) gt R` and `r_(2) gt R`
`(I_(1))/(I_(2))=((GM//r_(1)^(2)))/((GM//r_(2)^(2))) = (r_(2)^(2))/(r_(1)^(2))`
(b) `r_(1) lt R` and `r_(2) lt R`
`(I_(1))/(I_(2)) = ((GM//R^(3))r_(1))/((GM//R^(3))r_(2))=(r_(1))/(r_(2))`
(c ) `r_(1)gt R` and `r_(2)lt R`
`(I_(1))/(I_(2)) = ((GM//r_(1)^(2)))/((GM//R^(3))r_(2)) = (R^(3))/(r_(1)^(2)r_(2))`