A student performs an experiment to determine the Young's modulus of a wire , exactly `2 m` long , by Searle's method . In a particular reading , the student measures the extension in the length of the wire to be `0.8 mm` with an uncertainty of `0.05 mm` at a load of exactly `1.0 kg` . The student also measures the diameter of the wire to be `0.4 mm` with an uncertainity of `0.01 mm` . Take `g = 9.8 m s^(-2) ` ( exact) . The Young's modulus obtained from the reading is

Options

A. `(2.0+- 0.3)xx10^(11)N//m^(2)`
B. `(2.0+-0.2)xx10^(11)N//m^(2)`
C. `(2.0+- 0.1)xx10^(11)N//m^(2)`
D. `(2.0+-0.05)xx10^(11)N//m^(2)`

Explanation

`(mg)/(pir^(2)) = (Y) (x)/(l_(0))`
`Y = (mgl_(0))/(pi (d^(2))/(4)x) = 2 xx 10^(11) N//m^(2)`
`((DeltaY)/(Y))_(max)=2((Deltad)/(d))+(Deltax)/(x)=2((0.01)/(0.4))+(0.05)/(0.8)=(9)/(80)`
`DeltaY = (9)/(80) xx 2 xx 10^(11) = 0.225 xx 10^(11) N//m^(2) = 0.2 xx 10^(11)N//m^(2)` .