show that density of nucleons is independent to mass number.

let the volume of nucleus be =V, the mass of the nucleus be M, and the mass of nucleon = m

$V=\frac{4}{3}\pi r^3$
density =$$\begin{gathered} \rho =\frac{M}{V}, \\ M=\frac{4}{3}\pi r^3\rho \end{gathered}$$
As we know $$\begin{gathered} r=r_0{A}^{1/3} \\ {r}^3=r_0^{3}A \end{gathered}$$
$M=\frac{4}{3}\pi r_0^{3}A\rho$--------------(i)
As we know mass of nucleon =mA-----------(ii)
equating eqs (i) and (ii) we get
$$\begin{gathered} m=\frac{4}{3}\pi r_0^3\rho \\ \rho =\frac{3m}{4\pi r_0^3} \end{gathered}$$
Hence nuclear density is independent to mass number (A).