A slightly conical wire of length `l` and radii, `r_(1)` and `r_(2)` is strecthced by two forces each of magnitude `F` applied parallel to length in opposide directions and normal to end faces. If `Y` denotes the Young's modulus then find the elogation of the wire `(r_(2) gt r_(1))`.

Explanation

Consider and element of length `dx` at distance `x` as shown in the figures. The radius of the section `r_(x) = r_(1) + ((r_(2) - r_(1))/(l))x`
Extension of the element `d l = (F(dx))/(A_(x) Y) = (F dx)/(pi r_(x)^(2)Y)`
Elongation of total wire is
`l = int dl = int_(0)^(l) (Fdx)/(pi[r_(1) + (r_(2) - r_(1))/(l)x]^(2)Y) = (Fl)/(pi r_(1) r_(2) Y)`