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A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are $5.012 \mathrm{~m}$ and $5 \mathrm{~m}$ respectively at $27^{\circ} \mathrm{C}$. The temperature (in ${ }^{\circ} \mathrm{C}$ ) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ )
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227
Temperature to which the iron ring must be heated so to fit the wheel $\mathrm{T}^{\prime}=\frac{\mathrm{d}_{\mathrm{w}}-\mathrm{d}_{\mathrm{i}}}{\mathrm{d}_{\mathrm{i}} \alpha}+\mathrm{T}_1$ $=\frac{5.012-5}{5 \times 1.2 \times 10^{-5}}+27=\frac{1.2 \times 10^{-2}}{5 \times 1.2 \times 10^{-5}}+27^{\circ} \mathrm{C}=227^{\circ} \mathrm{C}$
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