Answer
$\lambda = 0.477~kg/m$
Work Step by Step
We can find the cross-sectional area of the wire:
$R = \frac{\rho~L}{A}$
$A = \frac{\rho~L}{R}$
$A = \frac{(2.75\times 10^{-8}~\Omega\cdot m)(1~km)}{0.150~\Omega}$
$A = 1.833\times 10^{-4}~m^2$
We can find the mass per unit length of the cable:
$\lambda = \rho~A$
$\lambda = (2600~kg/m^3)(1.833\times 10^{-4}~m^2)$
$\lambda = 0.477~kg/m$
