The coefficient of area expansion \(\beta\) of a rectangular sheet of a solid in terms of the coefficient of linear expansion \(\alpha\) is:
1. \(2\alpha\)
2. \(\alpha\)
3. \(3\alpha\)
4. \(\alpha^2\)

A blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are 5.012 m and 5.00 m, respectively at 27 °C. To what temperature should the ring be heated so as to fit the rim of the wheel?

(Given: $\mathrm{\alpha } \mathrm{for} \mathrm{iron}=1.20\times {10}^{-5} °{\mathrm{C}}^{-1}$)

1.   $128 °\mathrm{C}$

2.   $118 °\mathrm{C}$

3.   $227 °\mathrm{C}$ 

4.   $218 °\mathrm{C}$