Consider the following two statements,$A$ and $B$ and identify the correct answer given below:
$A$. Nuclear density is same for all nuclei.
$B$. Radius of the nucleus $R$ and its mass number $A$ are related as $\sqrt{A} \propto R^{1 / 6}$.

At what distance does the minimum value of potential energy be obtained between the nucleons (in $fm$)?

The unit of length convenient on the nuclear scale is a fermi: $1 \; f = 10^{-15} \; m$. Nuclear sizes obey roughly the following empirical relation: $r = r_{0} A^{1/3}$,where $r$ is the radius of the nucleus,$A$ is its mass number,and $r_{0}$ is a constant equal to about $1.2 \; f$. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of a sodium nucleus.

The mass number of $He$ is $4$ and the mass number of $S$ is $32$. How many times is the radius of the $S$ nucleus compared to the radius of the $He$ nucleus?

$A$ nucleus splits into two parts. If the ratio of their velocities is $8 : 1$, what is the ratio of their radii?

The Avogadro number is $6 \times 10^{23}$. What will be the number of protons,neutrons,and electrons in $14 \, g$ of $_6C^{14}$?