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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Topic Test - Thermometry, Thermal Expansion and Calorimetry (3-5-21)

  • question_answer
    Two rods, one of aluminum and the other made of steel, having initial length \[{{l}_{1}}\] and \[{{l}_{2}}\] are connected together to form a single rod of length \[{{l}_{1}}+{{l}_{2}}\]. The coefficients of linear expansion for aluminum and steel are \[{{\alpha }_{a}}\] and \[{{\alpha }_{s}}\] respectively. If the length of each rod increases by the same amount when their temperature are raised by  \[{{t}^{o}}C\], then find the ratio \[\frac{{{l}_{1}}}{({{l}_{1}}+{{l}_{2}})}\]

    A) \[\frac{{{\alpha }_{s}}}{{{\alpha }_{a}}}\]

    B) \[\frac{{{\alpha }_{a}}}{{{\alpha }_{s}}}\]

    C) \[\frac{{{\alpha }_{s}}}{({{\alpha }_{a}}+{{\alpha }_{s}})}\]

    D) \[\frac{{{\alpha }_{a}}}{({{\alpha }_{a}}+{{\alpha }_{s}})}\]

    Correct Answer: C

    Solution :

                   Given \[\Delta {{l}_{1}}=\Delta {{l}_{2}}\]  or \[{{l}_{1}}{{\alpha }_{a}}t={{l}_{2}}{{\alpha }_{s}}t\] \[\therefore \] \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{\alpha }_{s}}}{{{\alpha }_{a}}}\]  or  \[\frac{{{l}_{1}}}{{{l}_{1}}+{{l}_{2}}}=\frac{{{\alpha }_{s}}}{{{\alpha }_{a}}+{{\alpha }_{s}}}\].


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