Consider an element dx which is at a distance x from the end with r, as radius. Tfhe change in length in this portion is
dl = \((\frac{F}{A})\) \(\frac{dx}{Y}\)
From figure we can write radius at a distance x is, rx = r1 + x tanθ
⇒ A = π(rx)2
= π (r1 + x tanθ)2
Total extension
Total extension = \(\frac{F.L}{Yr_1r_2}\)
[∵ tanθ = \(\frac {r_2-r_1}{L}]\).
