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

Options

A. Due to the errors in the mesurement of `d` and `l` are the same
B. Due to the error in the measurement of `d` is twice to that of the error in the measurement of `l`
C. Due ot the error in the measurement of `l` is twice to that of the error in the measurement of `d`
D. Due to the error in the measurement of `d` is four time to that of the error in the measurement of `l`

Answer

A

Explanation

(1) `Y = (4 MLg)/(pi l d^(2))`
Least count = `(p it c h)/(n u m b e r of d i v i s i o n s o n c i r c u l a r s c a l e)`
`= (0.5)/(100) = 0.005 mm`
`(Delta Y)/(Y) = (Delta L)/(L) + (Delta g)/(g) + (Delta l)/(l) + 2 (Delta d)/(d)`
`(Delta l)/(l) = (0.005)/(0.5) = 0.02`
`2 (Delta d)/(d) = 2 xx (0.005)/(0.5) = 0.02`