Solution:
Length(l)=60cm=0.6m
Radius (r)=$\frac{4}{2}$cm=$2 \times {10^{ - 2}}$m
${\mu _r}$=400
Inductance of solenoid,
$\begin{array}{l}L = {\mu _0}{N^2}\frac{{Area}}{{Length}}\\L = {\mu _0}{N^2}\frac{{\pi {r^2}}}{l}\\L = 4\pi \times {10^{ - 7}} \times {(4000)^2} \times \frac{{\pi \times {{(2 \times {{10}^{ - 2}})}^2}}}{{0.6}}\\\therefore L = 0.042\end{array}$
Now
Inductance of solenoid when it has an iron core of
relative permeability is
$L' = {\mu _r}L = 400 \times 0.042 = 16.84H$