Question

An iron tyre is to be fitted onto a wooden wheel $100cm$ in diameter. The diameter of the tyre is $5mm$ smaller than that of the wheel. How much should the temperature (in ${}^{\circ }C$ ) of the tyre be increased for this purpose ? $\alpha$ for iron $=12\times 10^{-6}$ per ${}^{\circ }C$

Answer 1

Answer: 418.80

To fit the tyre, its diameter has to be increased from $99.5$ to $100$.
So let temperature to which tyre must be heated be $T$.
$\ell ={\ell }_0[1+\alpha \Delta \theta ]$
$100=99.5\left[1+12\times 10^{-6}T\right]$
$1.0050251=1+12\times 10^{-6}T$
$T=\frac{0.0050251}{12}\times 10^6=418.8^{\circ }C$