In the determination of Young's modulus `(Y = (4MLg)/(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 screw gauge and a micrometer, respectively. The 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. (a) due to the errors in the measurements of `d and l` are the same.
B. (b) due to the error in the measurement of `d` is twice that due to the error in the measurement of `l`.
C. ( c ) due to the error in the measurement of `l` is twice that due to the error in the measurement of `d`.
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

(a) The maximum possible error in `Y` due to `l and d` are
`(DeltaY)/(Y) = (Deltal)/(l)+(2Deltad)/(d)`
`Least count = (Pitch)/(No. of divi on circular scale)`
`=(0.5)/(100)mm = 0.005mm`
Error contribution of `l =(Deltal)/(l) = (0.005mm)/(0.25mm) = (1)/(50)`
`d =(Deltad)/(d) = (2xx(0.005mm))/(0.5mm) = (1)/(50)`