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 measurments of d and l are the same
B. due to the error in the measurements of d is twice that due to the error in the measurement of `l`
C. due to the erroe 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 error in the measurement of `l`

Answer

a

Explanation

`Deltad=Deltal=0.5/100mm`
`Y=(4MLg)/(pi ld^(2))((DeltaY)/Y)_(max)=(Deltal)/l+2(Deltad)/d`
Error due to `l` measurement, `(Deltal)/l=(0.5//100 mm)/(0.25 mm)`
Error due to d measurement, `2 (Delta d)/d=(2xx0.5/100)/(0.5 mm)=(0.5/100)/0.25`
So error in y due to `l` measurement = error in y due to d measurement.