The elastic limit of an alloy is 5.0×108 N/m2. What is the minimum radius rmin of a 4.0 m long wire made from the alloy if a single strand is designed to support a commercial sign that has a weight of 8000 N and hangs from a fixed point? To stay within safety codes, the wire cannot stretch more than 5.0 cm.

The radius is  

Explanation:

   From the question we are told that

      The  elastic limit(stress) is

      The length is  

      The weight of the commercial sign is    

       The maximum extension of the wire is  

Generally the elastic limit of an alloy (stress) is is mathematically represented as

Where A is the cross-sectional area of the wire which is mathematically represented as

here which is the minimum radius of the wire that support the commercial sign

So

=>      

substituting values