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In Searle's experiment to find young's m...

In Searle's experiment to find young's modulus, the diameter of wire is measured as `D = 0.05 cm` , the length of wire is `L = 125 cm` , and when a weight , `m = 20 kg` is the put , extension in wire was found to be `0.100 cm` . Find the maximum permissible error in Young's modulus (Y).

Text Solution

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`(mg)(pid^(2)//4) Y = (9x)/(l)rArr Y = Y=(mgl)/((pi//4)d^(2)x)`
`((dY)/(Y))_(max)=(Deltam)/(m)+(Deltal)/(l)+2(Deltad)/(d)+(Deltax)/(x)`
`m = 20.0kg rArr Deltam = 0.1kg`
`l = 125 m rArr Deltal = 1cm`
`d = 0.050 cm rArr Deltad = 0.001 cm`
`x = 0.100 cm rArr Deltax = 0.001 cm`
`((dY)/(Y))_(max)=((0.1kg)/(20.0kg)+(1cm)/(125cm)+(2xx0.001)/(0.05cm)+(0.001)/(0.100)(cm)/(cm))xx100%=6.3%` .
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