A close-coil helical spring is to have a stiffness of \(800 \mathrm{~N} / \mathrm{m}\) in compression, with a maximum load of \(40 \mathrm{~N}\) and a maximum shearing stress of 120 \(\mathrm{N} / \mathrm{mm}^{2}\). The solid length of the spring is \(48 \mathrm{~mm}\). Find the wire diameter, mean coil radius, and the number of coils. \(G=50,000 \mathrm{~N} / \mathrm{mm}^{2}\). (Assume shear stress is produced only due to the torque produced in the wire due to axial loading).