In the problem discussed in the text, find `E - r` expressions for inside and outside points.

Explanation

Inside points `(r le R)`
Directly substituting value of `m_(in)` from Eq. (ii) in Eq.(i) we have,
`E = (G)/(r_(2))[(4pi rho_(0) r^(5))/(5)]` ltbr or `E = (4 pi G rho_(0) r^(3))/(5)`
Outside points `(r ge R)`
Mass is only upto `r = R`. So, substituting `r = R` in Eq. (ii) we have,
`m_(in) = (4 pi rho_(0) )/(5)R^(5)`
Now, substituing this value of `m_(in)` in Eq. (i) we have
`E = (G)/(r_(2))[(4pi rho_(0) r^(5))/(5)]`
or `E = (4 pi G rho_(0) R^(5))/(5 r^(2))`