Question

An iron tyre is to be filled 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 of the tyre be increased for this purpose? $(\alpha$ for iron $=12\times {10}^{-6}{}^{\circ }{C}^{-1})$

Answer 1

Diameter of wooden wheel $100cm=1000mm$

Initial diameter of iron wheel is $1000-5=995mm$

Radius of iron wheel $r=995/2=497.5mm$

Increase in radius required $\Delta r=5/2=2.5mm$

We know

$\delta r=r\alpha \times \Delta T$

$2.5=497.5\times 12\times {10}^{-6}\Delta T$

$\Delta T={418.76}^{o}C$