A spherically symmetric charge distribution is characterised by a charge density having the following variation : \[\]$\;\rho(r)=\rho_{0}(1-\large\frac{r}{R})\;for\;r < \normalsize R\;$\[\]$\;\rho(r) =0 \;\; r \geq R\;$ \[\] where r is the distance from the center of the charge distribution and $\;\rho_{0}\;$ is a constant .The electric field at an internal point $(r < R)$ is :

Question

$(a)\;\large\frac{\rho_{0}}{4\in_{0}}\;(\large\frac{r}{3}-\large\frac{r^{2}}{4R})\qquad(b)\;\large\frac{\rho_{0}}{\in_{0}}\;(\large\frac{r}{3}-\large\frac{r^{2}}{4R})\qquad(c)\;\large\frac{\rho_{0}}{3\in_{0}}\;(\large\frac{r}{3}-\large\frac{r^{2}}{4R})\qquad(d)\;\large\frac{\rho_{0}}{12\in_{0}}\;(\large\frac{r}{3}-\large\frac{r^{2}}{4R})$