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In the determination of Young's modulus ...

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`Y=(4 MLg)/(pi ld^2)`
L.C. of screw gauge and micrometer
L.C `Deltad=DeltaI=(0.5)/100 = 5 xx10^(-3)mm`
`(DeltaY)/Y=(Deltal)/(l)+2(Deltad)/d implies(Deltal)/(l)xx100=(0.005)/(0.25)xx100=2%`
`implies 2(Deltad)/(d) xx100 = 2xx(0.005)/(0.5)xx100=2%`
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