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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Critical Thinking

  • question_answer
    An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The  diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is 3.6 × 10?5/ºC)   [CPMT 1989]

    A)            167ºC                                      

    B)            334ºC

    C)            500ºC                                      

    D)            1000ºC

    Correct Answer: C

    Solution :

                       Initial diameter of tyre = (1000 ? 6) mm = 994 mm, so initial radius of tyre \[R=\frac{994}{2}=497\,mm\] and change in diameter DD = 6 mm so \[\Delta R=\frac{6}{2}=3\,mm\] After increasing temperature by Dq tyre will fit onto wheel Increment in the length (circumference) of the iron tyre  DL = L ´ a ´ Dq  \[=L\times \frac{\gamma }{3}\times \Delta \theta \]         [As \[\alpha =\frac{\gamma }{3}]\] \[2\pi \,\Delta R=2\pi \,R\,\left( \frac{\gamma }{3} \right)\,\Delta \theta \]Þ\[\Delta \theta =\frac{3}{\gamma }\frac{\Delta R}{R}=\frac{3\,\times 3}{3.6\times {{10}^{-5}}\times 497}\]   Þ\[\Delta \theta ={{500}^{o}}C\]


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