Engineering
Physics
Errors
Question

In the determination of Young’s modulus  (Y=4MLgπld2)  by using Searle’s method, a wire of length L = 2m 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. 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

due to the errors in the measurements of d and ℓ are the same

due to the error in the measurement of d is four times that due to the error in the measurement of ℓ.

due to the error in the measurement of ℓ is twice that due to the error in the measurement of d.

due to the error in the measurement of d is twice that due to the error in the measurement of ℓ.

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Solution

 Δyy=ΔLL+Δℓ+2Δdd

ℓ = 0.25, d = 0.5