JEE Main & Advanced Physics Transmission of Heat Question Bank Critical Thinking

  • question_answer
    Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is                                                                   [UPSEAT 2002]

    A)            2 : p

    B)            1 : 2

    C)            p : 2

    D)            3 : 2

    Correct Answer: A

    Solution :

                       \[\frac{dQ}{dt}=\frac{KA\Delta \theta }{l}\], For both rods K, A and Dq are same    Þ \[\frac{dQ}{dt}\propto \frac{1}{l}\]So \[\frac{{{(dQ/dt)}_{semi\,circular}}}{{{(dQ/dt)}_{straight}}}=\frac{{{l}_{straight}}}{{{l}_{semicircular}}}=\frac{2r}{\pi \,r}=\frac{2}{\pi }\].


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