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AMU Medical AMU Solved Paper-2000

  • question_answer
    A steel wire of length 20 cm and uniform cross section 1 mm2 is tied rigidly at both the ends. If temperature of the wire is altered from \[40{}^\circ C\] to \[20{}^\circ C\]. Calculate the change in tension. (Given coefficient of linear expansion of steel \[\alpha =\text{1}.\text{1}\times {{10}^{-5}}/{}^\circ \text{C}\]and Youngs modulus Vfor steel \[=\text{ 2}\times \text{1}{{0}^{\text{11}}}\text{ N}/{{\text{m}}^{\text{2}}})\]

    A)  88 N                                     

    B)  UN

    C)  44 N                                     

    D)  22 N

    Correct Answer: C

    Solution :

                     The change in tension, when wire is cooled is given by                 \[F=yA\,\,\alpha \,\Delta \theta \] Given,   \[\Delta \theta ={{40}^{o}}-{{20}^{o}}={{20}^{o}}C\],                 \[A=1\,m{{m}^{2}}=1\times {{10}^{-6}}{{m}^{2}}\],                 \[\alpha =1.1\times {{10}^{-5}}{{/}^{o}}C\],                 \[Y=2\times {{10}^{11}}N/{{m}^{2}}\] \[\therefore \]  \[F=2\times {{10}^{11}}\times {{10}^{-6}}\times 1.1\times {{10}^{5}}\times 20\] \[\Rightarrow \]               F = 44 N


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