To solve this problem, we need to understand the concept of longitudinal stress in a wire.$\\$When a weight $W$ is attached to the free end of a wire suspended from a rigid support,$\\$the wire experiences a force due to the weight. This force is equal to the weight $W. \\$The longitudinal stress at any point of cross-sectional area $A$ of the wire is defined as$\\$the force applied per unit area. Mathematically, it is given by:$\\$Stress $= \frac{Force}{Area} \\$In this case, the force is the weight $W$ acting on the wire, and the area is $A. \\$Therefore, the longitudinal stress $\sigma$ is:$\\ \sigma = \frac{W}{A} \\$Thus, the correct option is Option 2: $\frac{W}{A}.$