A student performs an experiment to determine the Young's modulus of a wire, exactly`2m` long, by Searle's method. In a partcular reading, the student measures the extension in the length of the wire to be `0.8mm with an uncertainty of `+- 0.05mm` at a load of exactly `1.0kg`, the student also measures the diameter of the wire to be `04mm` with an uncertainty of `+-0.01mm`. Take `g=9.8m//s^(2)` (exact). the Young's modulus obtained from the reading is

Explanation

`Y = (F//A)/(Delta L //L)`
`A = pi r^(2) = pi ((d)/(2))^(2) = (pi d^(2))/(4)`
`Y = (4 F)/(pi d^(2) ((Delta L)/(L)))`
`(Delta Y)/(Y) = 2 (Delta d)/(d) + (Delta (Delta L))/((Delta L))`
` = 2 ((0.01)/(4)) + (0.05)/(0.8)`
`= 0.005 + 0.0625`
`Y = (4 F)/(pi d^(2) ((Delta L)/(L))) = (4 xx 1 xx 9.8)/(pi (0.4 xx 10^(-3))^(2) xxx ((0.8 xx 10^(-3))/(2)))`
`=1.94xx10^(11)`
`=2xx10^(11)N//m^(2)`
`DeltaY=0.2xx10^(11)N//m^(2)`
`Y=(2+-0.2)xx10^(11)N//m^(2)`