A body of mass 3.14 kg is suspended from one end of a non uniform wire of length 10m, such that the radius of the wire is changing uniformly from `9.8xx10^(-4)` m at one end to `5xx10^(-4)` m at the other end. Find the change in length of the wire in mm. Young's modulus of the material of the wire is `2xx10^(11)N//m^(2)` (mass of wire is negligible)

Explanation

`Y=(F//A)/(dy//dx),r=b-((b-a)/(L))x`
`r=b-tan theta x, A=pi(b-xtan theta)^(2)`
`int_(0)^(DeltaL)dy=(F)/(piY)int_(0)^(L)(dx)/((b-xtan theta)^(2))`
`Delta L=10^(-3)m=1mm`