To solve this problem, we need to find the expression for Young's modulus of the wire.$\\$Young's modulus $(Y)$ is defined as the ratio of tensile stress to tensile strain.$\\$Tensile stress is given by:$\\ \frac{Force}{Area} = \frac{Mg}{A} \\$where $M$ is the mass, $g$ is the acceleration due to gravity, and $A$ is the cross-sectional area.$\\$Tensile strain is given by:$\\ \frac{\Delta L}{L} = \frac{L_1 - L}{L} \\$where $\Delta L = L_1 - L$ is the change in length.$\\$Young's modulus $(Y)$ can be expressed as:$\\ Y = \frac{Tensile \ stress}{Tensile \ strain} \newline {} \\ Y = \frac{\frac{Mg}{A}}{\frac{L_1 - L}{L}} \\$Simplifying the expression:$\\ Y = \frac{Mg \cdot L}{A \cdot (L_1 - L)} \\$Thus, the expression for Young's modulus is:$\\ \frac{MgL}{A(L_1 - L)} \\$This corresponds to Option 3.