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`)

Options

A. `2.1%`
B. `3.2%`
C. `4.3%`
D. `5.4%`

Answer

C

Explanation

`(mg)/(pid^(2)//4)=Y((x)/(l))impliesY=(mgl)/((pi//4)d^(2)x)`
`((dY)/(Y))_(max)=(Deltam)/(m)+(Deltal)/(l)+2(Deltad)/(d)+(Deltax)/(x)`
`m=20.0 kg implies Deltam=0.1kg`
`l=125 mimpliesDeltal=1cm`
`x=0.100cm implies Deltax=0.001cm`
`((dY)/(Y))_(max)=((0.1kg)/(20.0kg)+(1cm)/(125cm)+(0.001cm)/(0.05cm)+(0.001cm)/(0.100cm))xx100=4.3%`