A wheel is 80.3 cm in circumference. An iron tyre measures 80.0 cm around its inner face. If the coefficient of linear expansion for iron is $12 imes 10^{- 6}℃^{- 1}$, the temperature of the tyre must be raised by

Question

A wheel is 80.3 cm in circumference. An iron tyre measures 80.0 cm around its inner face. If the coefficient of linear expansion for iron is $12 	imes 10^{- 6}℃^{- 1}$, the temperature of the tyre must be raised by

Dr. Abubacker · Accepted Answer

(c) Here, $\mathrm{\Delta}l = 80.3 - 80.0 = 0.3\ $cm
$l = 80\ cm,\ \alpha = 12\  	imes 10^{- 6}℃^{- 1}$
Rise in temperature $\mathrm{\Delta}T = \frac{\mathrm{\Delta}l}{l\alpha}$
$\mathrm{\Delta}T = \ \frac{0.3}{80 	imes 12 	imes 10^{- 6}} = 312.5℃$

Q. A wheel is 80.3 cm in circumference. An iron tyre measures 80.0 cm around its inner face. If the coefficient of linear expansion for iron is $12 \times 10^{- 6}℃^{- 1}$, the temperature of the tyre must be raised by

Explanation

Reviewed by Dr. Abubacker

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