Question

An iron tire is to be filled onto a wooden wheel $100cm$ in diameter. The diameter of the tire is $5mm$ smaller than that of the wheel. How much should the temperature of the tire be increased for this purpose? ($\alpha$ for iron $=12\times {10}^{-6}{}^o{C}^{-1})$.

Answer 1

Initial diameter of tyre $=(1000?6)mm=994mm$, so initial radius of tyre

$R=9942=497mm$

and change in diameter $DD=6mm$ so

$\Delta R=62=3mm$
After increasing temperature by Dq tyre will fit onto wheel Increment in the length (circumference) of the iron tyre DL = L

$L\times \gamma 3\times \Delta \theta$

$\alpha =\gamma 3$

$2\pi \Delta R=2\pi R\left(\gamma 3\right)\Delta \theta$

$\Delta \theta =3\gamma \Delta RR=3\times 33.6\times 10=5\times 497$

$\Delta \theta ={500}^{0}C$