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

Answer

A, B, D

Explanation

`Y = (4FL)/(pid^2l)=(4 xx 1.0 xx 9.8 xx 2)/((pi)(0.4 xx 10^-3)^2(0.8 xx 10^-3)`
=`1.94 xx 10^11 N//m^2`
Futher, `Y = (4MgL)/(pid^2l)`
`rArr (DeltaY)/Y=2((Deltad)/d)+(Deltal)/l`
or `DeltaY = [2((Deltad)/d)+((Deltal)/l)] xx Y`
= `[2 xx ((0.01)/(0.4))+((0.05)/(0.8))] xx 1.94 xx 10^11`
= `0.22 xx 10^11 N//m^2`.