Question

A body of mass 3.14 kg is suspended from one end of a wire of length 10.0 m. The radius of the wire is changing uniformly from 9.8 × 10^–4 m at one end to 5.0 × 10^–4 m at the other end. Find the change in the length of the wire. What will be the change in length if the ends are interchanged? Young’s modulus of the material of the wire is 2 × 10¹¹ N/m² .

Answer 1

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 = r₂ -r₁/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.