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Question

# In the determination of Young’s modulus (Y=4 MLgπl d2) 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. Quantities 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 contributions to the maximum probable error of the Y measurement is:

A

Due to the errors in the measurement of d and l are the same

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B

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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C

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

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D

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

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Solution

## The correct option is A Due to the errors in the measurement of d and l are the same From the formula for Young's modulus, ΔYY=Δll+2Δdd Here both screw gauge and micrometer used have same least count and hence the maximum probable error in the measurement of l and d will be same i.e., Δl=Δd=Δx The error contribution to measured Y from error in d is ed=2Δdd=2Δx0.5=Δx0.25 The error contribution to measured Y from error in l is el=Δll=Δx0.25

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