In the determination if Young's modulus `((Y = (4MLg)/(pild^(2))` by using searle's method, a wire of length `L=2m` and diameter `d=0.5mm` is used. For a load `M=2.5kg`, an extension `l=0.25mm` in the length of the wire is observed. Quantites `D and l` are measured using a screw gauge and a micrometer, respectively. they have the same pitch of `0.5mm`. the number of divisions on their circular scale is `100`. the contrubution to the maximum probable error of the `Y` measurement

Options

A. due to the errors in the mesurement of `d` and `l` are the same
B. due to the error in the measurement of `d` is twice that due to the error in the meaurement of `l`
C. due to the error in the measurement of `l` is twice that due to the error in the measurement of `d`.
D. due to the error in the measurement of `d` is four times that due to the error in the measurement of `l`.

Answer

A

Explanation

`L.C=(0.5)/(100)=0.005mm`
`(DeltaY)/(Y)=(Deltal)/(l)+(2Delta(d))/(d)`, `(Deltal)/(l)=(0.005xx10^(-3))/(0.25xx10^(-3))=(1)/(50)`
`2(Delta(d))/(d)=(2xx0.005xx10^(-3))/(0.5xx10^(-3))=(1)/(50)`