JEE Main & Advanced JEE Main Paper (Held On 8 April 2017)

  • question_answer
    A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increases by \[\Delta T.\] The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and \[\alpha \] its coefficient of linear expansion. Then, F is equal to -                 [JEE Online 08-04-2017]

    A) \[IAY\alpha \Delta T\]                   

    B) \[AY\alpha \Delta T\]

    C) \[\frac{AY}{\alpha \Delta T}\]                    

    D) \[{{I}^{2}}Y\alpha \Delta T\]

    Correct Answer: C

    Solution :

    Net change in length = 0 Thermal Exp. \[=I\propto \Delta t\] \[y=\frac{F/A}{\Delta l/l}\] \[\frac{\Delta l}{l}=\frac{F}{Ay}\] \[\frac{Fl}{Ay}=l\propto \Delta t\] \[F=Ay\propto \Delta t\]             


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