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The yield strength of an alloy is \( 5.0 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2} \). What is the minimum radius \( r_{\text {min }} \) of a \( 3.0 \mathrm{~m} \) long wire made from the alloy if a single strand is designed to support a commercial sign that has a weight of \( 8000 \mathrm{~N} \) and hangs from a fixed point? To stay within safety codes, the wire cannot stretch more than \( 5.0 \mathrm{~cm} \) \( r_{\min } \)