A student performs an experiment to determine the Young's modulus of a wire, exactly 2m long, by Searle method, In a particular reading, the student measures the extension in the length of the wire to be 0.8mm wi an uncertainty of `pm`0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire the 0.4mm with an uncertainty of `pm`0.01 mm. Take g=9.8 `ms^(-2)` (exact). The Young's modulus obtained fro the reading is

Options

A. `(2.0pm0.3)xx10^(11) Nm^(-2)`
B. `(2.0pm0.2)xx10^(11) Nm^(-2)`
C. `(2.0pm0.1)xx10^(11) Nm^(-2)`
D. `(2.0pm0.05)xx10^(11) Nm^(-2)`

Answer

B

Explanation

Young.s modulus Y =`(FL)/(AI)=(4FL)/(pid^(2)l)=2xx10^(11) nm^(-2)`
Further `(triangley)/(y)=2{2(triangled)/(d)+(trianglel)/(l)}y`
`{2xx0.01/0.4+0.05/0.8}xx2.0xx10^(11)=0.2xx10^(11)Nm^(-2) therefore y=(2.0 pm2)10^(11)`