2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Thermometry, Calorimetry & Thermal Expansion

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

  • question_answer
    Coefficient of linear expansion of brass and steel rods are \[{{\alpha }_{1}}\]and \[{{\alpha }_{2}}\]. Lengths of brass and steel rods are \[{{\ell }_{1}}\] and \[{{\ell }_{2}}\] respectively. If \[({{\ell }_{1}}-{{\ell }_{2}})\]is maintained same at all temperatures, which one of the following relations holds good?

    A) \[3{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]  

    B)        \[4{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]

    C) \[2{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]   

    D)        \[{{\alpha }_{1}}{{\ell }_{1}}={{\alpha }_{2}}{{\ell }_{2}}\]

    Correct Answer: D

    Solution :

    [d] From question, \[({{\ell }_{2}}-{{\ell }_{1}})\] is maintained same at all temperatures hence changed in length for both rods should be same i.e., \[\Delta {{\ell }_{1}}=\Delta {{\ell }_{2}}\]  As we know, coefficient of linear expansion \[\alpha =\frac{\Delta \ell }{{{\ell }_{0}}\Delta \ell }\]  \[{{\ell }_{1}}{{\alpha }_{1}}\Delta T={{\ell }_{2}}{{\alpha }_{2}}\Delta T\Rightarrow {{\ell }_{1}}{{\alpha }_{1}}={{\ell }_{2}}{{\alpha }_{2}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner