Overall changes in volume and radii of a uniform cylindrical steel wire 0.2% and 0.002% respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is?

If the volume is increasing by 0.2%, and the radius is decreasing by 0.002%, that means the wire is stretching by about 0.24%, which is the strain ( \epsilon) on the wire. Now you can use Hooke's Law of Elasticity and Young's modulus for steel to calculate the required stress to cause that strain: \sigma = E \epsilon.