In Searle's exp to find Young's modulus, the diameter of wire is mesured as `D=0.05cm` length of wire is `L=125cm`, and when a weight, `m=20.0 kg` is put, extension in wire was found to be `0.100cm`. Find maximum permissible percentage error in Young's modulus (`Y`)
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`( mg)/( pi d^(2) //4) = Y ((x)/(l)) rArr Y = ( mgl)/(( pi // 4)d^(2) x)` `((dY)/( Y)) _(max) = ( Delta m)/( m) + ( Delta l)/( l) + 2 ( Delta d)/(d) + ( Delta x)/(x)` ` m = 20.0 kg rArr Delta m = 0.1 kg` `l = 125 m rArr Delta l = 1 cm` `d = 0.050 cm rArr Delta d = 0.001 cm` `x = 0.100 cm rArr Delta x = 0.001 cm` `((dY)/( Y))_(max)` `= ((0.1 kg )/ ( 20.0 kg) + (1 cm)/( 125 cm) + (0.001 cm)/(0.05 cm) + (0.001 cm) /(0.100 cm)) xx 100 %` ` = 4.3%`
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