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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A brass rod of length 500 mm and diameter 3  mm is joined to a steel rod of same length and  diameter at \[\text{50}{{\,}^{\text{o}}}\text{C}\text{.}\]If the coefficients of linear expansion of brass and steel are \[2.5\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}}\]and \[1.25\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}},\] then change in length of the combined rod at \[200{{\,}^{o}}C\]is :

    A)  2.4 mm               

    B)  2.8 mm

    C)  3.2 mm               

    D)  3.6 mm

    Correct Answer: B

    Solution :

                     Change in length of brass rod \[\Delta {{l}_{B}}={{\alpha }_{B}}{{l}_{B}}({{T}_{2}}-{{T}_{1}})\] \[=2.5\times {{10}^{-5}}\times 500\times (200-50)\] \[=1.875\,mm\] Similarly change in length of steel rod \[\Delta {{l}_{S}}={{\alpha }_{S}}{{l}_{S}}({{T}_{2}}-{{T}_{1}})\]                 \[=1.25\times {{10}^{-5}}\times 500\times (200-50)\]                 \[=0.9375\,mm\] Therefore, change in length of the combined rod \[=\Delta {{l}_{B}}+{{l}_{S}}=1.875+0.9375\]                 \[=2.8125\,mm=2.8\,mm\]


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