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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Sample Paper Topic Test - Thermometry, Calorimetry & Thermal Expansion

  • question_answer
    Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be (\[{{\alpha }_{1}},{{\alpha }_{2}}\]= linear expansion co-efficient \[{{\text{A}}_{\text{1}}}\text{,}{{\text{A}}_{\text{2}}}\] =Area of rods \[{{\text{Y}}_{\text{1}}}\text{,}{{\text{Y}}_{\text{2}}}\]= Young modulus)

    A) \[\frac{{{\text{A}}_{\text{1}}}}{{{\text{A}}_{\text{2}}}}\text{=}\frac{{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{1}}}{{\text{Y}}_{\text{1}}}}{{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{2}}}{{\text{Y}}_{\text{2}}}}\]                

    B) \[\frac{{{\text{A}}_{\text{1}}}}{{{\text{A}}_{\text{2}}}}\text{=}\frac{{{\text{L}}_{1}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{1}}}{{\text{Y}}_{\text{1}}}}{{{\text{L}}_{2}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{2}}}{{\text{Y}}_{\text{2}}}}\]

    C) \[\frac{{{\text{A}}_{\text{1}}}}{{{\text{A}}_{\text{2}}}}\text{=}\frac{{{\text{L}}_{2}}{{\text{ }\!\!\alpha\!\!\text{ }}_{2}}{{\text{Y}}_{2}}}{{{\text{L}}_{1}}{{\text{ }\!\!\alpha\!\!\text{ }}_{1}}{{\text{Y}}_{1}}}\]      

    D) \[\frac{{{\text{A}}_{\text{1}}}}{{{\text{A}}_{\text{2}}}}\text{=}\frac{{{\text{ }\!\!\alpha\!\!\text{ }}_{2}}{{\text{Y}}_{2}}}{{{\text{ }\!\!\alpha\!\!\text{ }}_{1}}{{\text{Y}}_{1}}}\]

    Correct Answer: D

    Solution :

    \[Y=\frac{\text{Stress}}{\text{Strain}}=\frac{T/A}{\Delta \ell /\ell }\]
    \[\text{T=}\frac{\text{Y}\text{. }\!\!\Delta\!\!\text{ l}}{\text{l}}\text{A=Y}\text{.A  }\!\!\alpha\!\!\text{   }\!\!\Delta\!\!\text{ T}\]
    In both the rods tension will be same so
    \[{{\text{T}}_{\text{1}}}\text{ = }{{\text{T}}_{\text{2}}}\]
    Hence \[{{\text{Y}}_{\text{1}}}{{\text{A}}_{\text{1}}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{1}}}\text{ }\!\!\Delta\!\!\text{ T = }{{\text{Y}}_{\text{2}}}{{\text{A}}_{\text{2}}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{2}}}\text{ }\!\!\Delta\!\!\text{ T}\]
    \[\frac{{{\text{A}}_{\text{1}}}}{{{\text{A}}_{\text{2}}}}\text{=}\frac{{{\text{Y}}_{\text{2}}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{2}}}}{{{\text{Y}}_{\text{1}}}{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{1}}}}\]


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