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 `0.4mm` with an uncertainty of `+-0.01mm`. Take `g=9.8m//s^(2)` (exact). the Young's modulus obtained from the reading is

Options

A. `(2.0+-0.2)xx10^(11)Nm^(-2)`
B. `(2.0+-0.2)xx10^(11)Nm^(-2)`
C. `(2.0+-0.1)xx10^(11)Nm^(-2)`
D. `(2.0+-0.05)xx10^(11)Nm^(-2)`

Answer

B

Explanation

Young.s modulus `Y=(FL)/(Al)=(4FL)/(pid^(2)l)=((4)(1xx9.8)(2))/(pi(0.4xx10^(-3))^(2)(0.8xx10^(-3)))=2xx10^(11)Nm^(-20`
Further `(DeltaY)/Y=2((Deltad)/d)+((Deltal)/l),DeltaY={2((Deltad)/d)+((Deltal)/l)}Y`
`{2xx0.01/0.4+0.05/0.8}xx2.0xx10^(11)=0.2xx10^(11)Nm^(-2)" ":.y=(2.0+-2)10^(11)`