An iron wire AB of length `3 m` at `0^(@)C` is stretched between the oppsote walls of a brass casing at `0^(@)C`. The diameter of the wire is `0.6mm`. What extra tension will be set up in the wire when the temperature of the system is rasied to `40^(@)C`?
Given `a_("brass")=18xx10^(-6)//k`
`a_("iron")=12xx10^(-6)//K`
`Y_("iron=21xx10^(10)N//m^(2)`

Explanation

To solve the problem of finding the extra tension set up in the iron wire when the temperature is raised from \(0^\circ C\) to \(40^\circ C\), we can follow these steps:

### Step 1: Identify the given values
- Length of the iron wire, \(L = 3 \, m\)
- Diameter of the wire, \(d = 0.6 \, mm = 0.6 \times 10^{-3} \, m\)
- Coefficient of linear expansion of brass, \(\alpha_{brass} = 18 \times 10^{-6} \, K^{-1}\)
- Coefficient of linear expansion of iron, \(\alpha_{iron} = 12 \times 10^{-6} \, K^{-1}\)
- Young's modulus of iron, \(Y_{iron} = 21 \times 10^{10} \, N/m^2\)
...