How the rigidity modulus varies if the radius of the wire is doubled?

The rigidity modulus, also known as the shear modulus, is a material property that measures its response to shear stress. It is independent of the dimensions of the wire, such as its radius. Therefore, if the radius of the wire is doubled, the rigidity modulus remains unchanged. The deformation behavior of the wire may change due to the increased cross-sectional area, but the rigidity modulus itself is a constant for that material.