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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Self Evaluation Test - Thermal Properties of Matter

  • question_answer
    A steel rail of length 5 m and area of cross-section \[40 c{{m}^{2}}\]is prevented from expanding along its length while the temperature rises by \[10{}^\circ C\]. If coefficient of linear expansion and Young's modulus of steel are \[1.2\times l{{0}^{-5}} {{K}^{-1}}\] and \[2\times 1{{0}^{11}}\]\[{{\operatorname{Nm}}^{-2}}\] respectively, the force developed in the rail is approximately:                  

    A) \[2\times 1{{0}^{7}}N\]

    B) \[1\times 1{{0}^{5}}N\]

    C) \[2\times 1{{0}^{9}}N\]           

    D) \[3\times 1{{0}^{-5}}N\]

    Correct Answer: B

    Solution :

    [b] Young's modulus \[=\frac{Thermal\text{ }stress}{Stain}=\frac{F/A}{\Delta L/L}\] \[Y=\frac{F}{A.\alpha .\Delta \theta }\left( \because \frac{\Delta L}{L}\alpha \,\Delta \theta  \right)\] Force developed in the rail \[F=Y\,\alpha \,\Delta t\] \[=2\times l{{0}^{11}}\times 40\times l{{0}^{-4}}\times l.2\times 1{{0}^{-5}}\times 10\] \[=9.6\times {{10}^{4}}=1\,\times l{{0}^{5}}N\]


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