A blacksmith fixes iron ring on the rim of the wooden wheel of a … - Vidyadip

Question

A blacksmith fixes iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243 m$ and $5.231 m$, respectively at $27 ^\circ C$. To what temperature should the ring be heated so as to fit the rim of the wheel?

✓

Answer

Given,
$T_1=27^{\circ} C$
$L_{ T 1}=5.231 m$
$L_{ T 2}=5.243 m$
So,
$L_{T2}=L_{T1}\left[1+\alpha_1\left(T_2-T_1\right)\right]$
$5.243 m =5.231 m \left[1+1.2010^{-5} K ^{-1}\left(T_2-27^{\circ} C \right)\right]$
$\text { or } T_2=218^{\circ} C .$

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