A) \[167{}^\circ C\]
B) \[334{}^\circ C\]
C) \[500{}^\circ C\]
D) \[1000{}^\circ C\]
Correct Answer: C
Solution :
[c] Initial diameter of tyre =(1000 - 6) mm =994 mm, so initial radius of tyre \[\operatorname{R}=\frac{994}{2}= 497mm\] and change in diameter \[\Delta D = 6 mm\]so \[\Delta R =\frac{6}{2} = 3 mm\] After increasing temperature by \[\Delta \theta \]tyre will fit onto wheel Increment in the length (circumference) of the iron tyre \[\Delta L=L\times \alpha \times \Delta \theta =L\times \frac{\gamma }{3}\times \Delta \theta \left[ As\alpha =\frac{\gamma }{3} \right]\] \[2\pi \,\Delta R=2\pi R\left( \frac{\gamma }{3} \right)\Delta \theta \Rightarrow \Delta \theta \] \[=\frac{3}{\gamma }\frac{\Delta R}{R}=\frac{3\times 3}{3.6\times {{10}^{-5}}\times 497}\Rightarrow \Delta \theta \simeq {{500}^{\operatorname{o}}}C\]
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