In the experiment of Young's modulus `( Y = ( 4 MLg)/( pi //d^(2)))` by using Searle's method , a wire of length `L = 2 m and diameter d = 0.5 mm` is used . For a load `M = 2.5 kg` , an extension `l = 0.25 mm` in the length of the wire is observed. Quantities `d and l` are measured using a srew gauge and a micrometer , respectively. They have the same pitch of `0.5 mm `. The number of divisions on their circular scale is `100`. The contributions 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 .