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JEE PHYSICS MCQ: THERMAL PROPERTIES OF MATTER

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A large steel wheel is to be fitted on to a shaft of the same material. At 27∘C27^{\circ} \mathrm{C}, the outer diameter of the shaft is 8.70 cm8.70 \mathrm{~cm} and the diameter of the central hole in the wheel is 8.69 cm8.69 \mathrm{~cm}. The shaft is cooled using 'dry ice' (solid carbon dioxide). At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range. αsteel =1.20×10−5 K−1.\alpha_{\text {steel }}=1.20 \times 10^{-5} \mathrm{~K}^{-1} .
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Correct option: A
−68.8∘C-68.8^{\circ} \mathrm{C}
Option A (−68.8∘C-68.8^{\circ} \mathrm{C}) is correct because it is the temperature at which the shaft's diameter shrinks enough for the wheel to slip on.

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