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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2007

  • question_answer
    A wire of cross-sectional area 3 mm2 is first stretched between two fixed points at a temperature of \[20{}^\circ C\]. Determine the tension when the temperature falls to \[10{}^\circ C\]. Coefficient of linear   expansion  \[a={{10}^{5}}{{\,}^{\text{o}}}{{\text{C}}^{-1}}\]and

    A)  20 N                                     

    B)  30 N

    C)  60 N                                       

    D)  120 N

    Correct Answer: C

    Solution :

    Given,\[A=3m{{m}^{2}}=3\times {{10}^{-6}}{{m}^{2}}\] \[\alpha ={{10}^{-5}}^{o}{{C}^{-1}},\]     \[Y=2\times {{10}^{11}}N/{{m}^{2}}\]                 \[\Delta t={{(20-10)}^{o}}C\]                 \[={{10}^{o}}C\] Tension in the wire                 \[F=YA\,\alpha \,\Delta t\]                 \[=2\times {{10}^{11}}\times 3\times {{10}^{-6}}\times {{10}^{-5}}\times 10\]                 \[=60N\]


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