A steel wire of mass `mu` per unit length with a circular cross-section has a radius of `0.1cm`. The wire is of length `10m` when measured lying horizontal, and hangs from a hook on the wall. A mass fo `25kg` is hung from the free end of the wire. Assume the wire to be uniform and laterla strain `lt lt` logitudinal strain. If density of steel is `7860 kg m^(-3)` and Young's modulus is `2xx10^(11) N//m^(2)` then the extension in the length fo the wire is

Options

A. `1xx10^(-3)m`
B. `2xx10^(-3)m`
C. `3xx10^(-3)m`
D. `4xx10^(-3)m`

Answer

D

Explanation

Suppose `Delta L_(1)` is the extension in the wire of length `L` due to its mass. Then,
`Delta L_(1) = ((mg)(L//2))/(YA) = (mgL)/(2YA)`
where `m = pi r^(2) L rho`
Suppose `Delta L_(2)` is the extension in the wire due to hanged mass `M`.
`Delta L = Delta L = Delta L_(1) + Delta L_(2) = (mgL)/(2YA) + (MgL)/(YA)`
`Delta L = (gl)/(YA) ((m)/(2) + M)`
`Delta L = (10xx10)/(2xx10^(-11)xx3.14xx10^(-6)) (0.125+25)`
`= 4xx10^(-3)m`