The magnitudes of gravitational field at distances `r_(1)` and `r_(2)` from the centre of a uniform sphere of
adius 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 lt R.`

Explanation

In case of spherical volume distribution of mass `I=("GM")/(r^(2))"for"" " rgt R`
`and I=("GM")/(R^(3))r " for"" "r lt R`
(a) As both `r_(1)` and `r_(2)`are greater than R,
`(I_(1))/(I_(2))=(("GM"//r_(1)^(2)))/(("GM"//r_(2)^(2)))=(r_(2)^(2))/(r_(1)^(2))`
As both `r_(1)` and `r_(2)` are lesser than R.
`(I_(1))/(I_(2))=(("GM"//R^(3))r_(1))/(("GM"//R^(3))r_(2))=(r_(1))/(r_(2))`