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 erros in the measurment of d and l are the same
B. due to the error in themeasurments of d is twice that due to the error in the measurment of
C. due to the error in themeasurments of d is twice that due to the error in the measurment of
D. due to the error in themeasurments of d is twice that due to the error in the measurment of

Explanation

`Deltad = Deltal = (0.5)/(100)mm`
`y = (4MLg)/(pil d^(2))`
`((Deltay)/(y))_(max)=(Deltal)/(l)+2(Deltad)/(d)`
error due to l measurement `(Deltal)/(l) = (0.5//100mm)/(0.25mm)`
error due to measurement `2 (Deltad)/(d) = (2xx(0.5)/(100))/(0.5mm)=(0.5//100)/(0.25)`
So error in y due to l measurment = error in y due to d measurement .