Two structural cylindrical rods, $A$ and $B$, are designed to support a suspended platform.

Rod $A$ has a diameter $d$, length $L$, and mass $m$. It is manufactured from an alloy of density $\rho$ and Young modulus $E$.

Rod $B$ is designed to have the same mass $m$ and length $L$ as Rod $A$, but has a diameter of $4d$. Under the same tensile load, both rods undergo the exact same elastic extension.

Determine, in terms of $\rho$ and $E$:

1. The density of the alloy from which Rod $B$ is made.
2. The Young modulus of the alloy from which Rod $B$ is made.