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In the determination if Young's modulus ...

In the determination if Young's modulus `((Y = (4MLg)/(pild^(2))` 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. Quantites `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 contrubution to the maximum probable error of the `Y` measurement

A

due to the error in the measurements of `d and l` are the same.

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`Delta d = Delta l = ( 0.5)/( 100) mm y = ( 4 MLg)/( pi //d^(2)) (( Delta y)/(y))_(max) = ( Delta l)/(l) + 2 ( Delta d)/(d)`
Error due to `l` measurement , ` ( Delta l)/(l) = ( 0.5 // 100 mm)/( 0.25 mm)`
Error due to `d` measurement , `2 ( Delta d)/( d) = ( 2 xx ( 0.5)/( 100))/( 0.5 mm) = ( 0.5 // 100)/( 0.25)`
So error in `y` due to `l` measurement = error in `y` due to `d` measurement
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