The whole space is divided into 3 regions
1) $0 < r< R_1 \qquad F(r)=0$
2) $R_2 < r< R_2 \qquad F(r)=\large\frac{4}{3} $$\pi G\rho m \bigg( r - \large\frac{R_1^3}{r^2}\bigg)$
3) $R_2 < r< \infty \qquad F(r)=\large\frac{4}{3} $$\pi G\rho m \bigg( \large\frac{R_2^3-R_1^3}{r}\bigg)$
In region 1 - $F=0$
In region 2 - $F$ increase gradually
In region 3 - $F$ decrease gradually
Hence c is the correct answer.