There is a solid sphere of radius $R$ having uniformly distributed charge throughout it. What is the relation between electric field $E$ and distance $r$ from the centre (where $r < R$)?

The electric field in a region is radially outward with magnitude $E = A r_0$. The charge contained in a sphere of radius $r_0$ centered at the origin is

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution,there is a finite value of electric potential at the centre of the sphere,at the surface of the sphere,and also at a point outside the sphere. The electric potential at infinity is zero.
Statement-$1$: When a charge $q$ is taken from the centre to the surface of the sphere,its potential energy changes by $\frac{q \rho R^2}{6 \epsilon_0}$.
Statement-$2$: The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \epsilon_0}$.

$A$ thin metallic spherical shell of radius $r$ contains a charge $Q$ on its surface. $A$ point charge $q_1$ is placed at the centre of the shell and another charge $q_2$ is placed outside the shell at a distance $x$ from the centre. Then, the forces on charges $q_1$ and $q_2$ respectively are

The charge density of a uniformly charged infinite plane is $\sigma$. $A$ simple pendulum is suspended vertically downward near it. $A$ charge $q_0$ is placed on the metallic bob. If the angle made by the string with the vertical direction is $\theta$,then . . . . . . .

Obtain Coulomb's law from Gauss's law.