Given,

Volume of iron rod is, $V={10}^{-3} {\mathrm{m}}^3$

Relative permeability, ${\mu }_r=1000$

No of turns per unit length of solenoid is, $n=\frac{N}{l}=10 \mathrm{turns} {\mathrm{cm}}^{-1}=1000 \mathrm{turns} {\mathrm{m}}^{-1}$

Current through the solenoid is, $i=0.5 \mathrm{A}$

Magnetic moment of an iron core solenoid is given by,

$M=({\mu }_r-1) NiA$

$\Rightarrow M=\left({\mu }_r-1\right)Ni\frac{V}{l}=\left({\mu }_r-1\right)\frac{N}{l}iV$

$\Rightarrow M=\left(1000-1\right)\times 1000\times 0.5\times {10}^{-3}$

$\Rightarrow M=499.5\approx 500 \mathrm{A} {\mathrm{m}}^2$