During Searle's experiment, zero of the Vernier sacle lies between `3.20 xx 10^(-2),` and `3.25 xx 10^(-2)m` of the main scale. The `20^(th)` division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of `2kg` is applied to the wire, the zero of the vernier scale still lies between `3.20 xx 10^(-2),` and `3.25 xx 10^(-2)m` of the main scale but now the `45^(th)` division of Vernier scale coincide with one of the main scale divisions. the length of the thin metallic wire is `2m` and its cross-sectional ares is `8 xx 10^(-7)m^(2)`. the least count of the Vernier scale is `1.0 xx 10^(-5)m`. the maximum percentage error in the Young's modulus of the wire is

Explanation

Observation -1 Let weight used is `W_(1)` extension `l_(1)`
`Y = (W_(1)//A)/(l_(1)//L)rArrW_(1)=(yAl_(1))/(L)l_(1)=3.2xx 10^(-2)+20xx10^(5)`
Observation -2 Let weight used is `W_(2)` extension `l_(2)`
Let weight used is `W_(2)` extension `l_(2)`
`y=(W_(2)//A)/(l_(2)//L)rArrW_(1)=(yAl_(2))/(L) l_(1) = 3.2 xx 10^(-2) + 45 xx 10^(-5)`
`((Deltay)/(y))_(max)=(Deltal)/(l)=(1xx10^(-5))/(25 xx 10^(-5))`
`((Deltay)/(y))_(max)xx100% = (1)/(25)100%=4%` .