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 pm 0.3) xx 10^(11) N//m^(2)`
B. `(2.0 pm 0.2) xx 10^(11) N//m^(2)`
C. `(2.0 pm 0.1) xx 10^(11) N//m^(2)`
D. `(2.0 pm 0.05) xx 10^(11) N//m^(2)`

Answer

B

Explanation

`Y=(Fl)/(A Deltal)=(Mgl)/(A Deltal)=((1)(9.8)(2))/(pi(0.2xx10^(-3))^(2)(0.8xx10^(-3)))`
`1.95 xx10^(11) =2.0 xx10^(11) Nm^(-2)`
`(DeltaY)/(Y)=(Delta(Deltal))/(Deltal)+2(Deltar)/(r)=(0.05)/(0.8)+2((0.01)/(0.4))`
`0.0625 +0.05=0.1125`
`DeltaY=(2.0xx10^(11)(0.1125)=0.2xx10^(11)`
`rArr Y=(2pm10^(11))(0.1125)=0.2xx10^(11)`
`rArr Y = (2pm 0.2)xx10^(11) Nm^(-2)`.