Since the radius of the wire changes uniformly, the gradient of the radius is constant over the whole length of the wire, i.e.,

dr/dx = r_{2} -r_{1}/L = K (say)

Consider a small element of the wire of length dx and radius r at a distance x from the upper end. The extension produced in the length of this element due to the weight of the body is

Total extension of the wire

It is obvious that the extension remains the same on interchanging the ends of the wire.