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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Mechanical Properties of Solids

  • question_answer
    A copper wire of length 1.0m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the Young's modulii of copper and steel are respectively \[1.0\times {{10}^{11}}N{{m}^{-2}}\] and \[2.0\times {{10}^{11}}N{{m}^{-2}}\], the total extension of the composite wire is:

    A) 1.75 mm

    B) 2.0 mm

    C) 1.50 mm

    D) 1.25 mm

    Correct Answer: D

    Solution :

    [d] \[{{Y}_{c}}\times (\Delta {{L}_{c}}/{{L}_{c}})={{Y}_{s}}\times (\Delta {{L}_{s}}/{{L}_{s}})\] \[\Rightarrow \,\,1\times {{10}^{11}}\times \left( \frac{1\times {{10}^{-3}}}{1} \right)=2\times {{10}^{11}}\times \left( \frac{\Delta {{L}_{s}}}{0.5} \right)\] \[\therefore \,\,\,\Delta {{L}_{s}}=\frac{0.5\times {{10}^{-3}}}{2}=0.25mm\] Therefore, total extension of the composite wire \[=\Delta {{L}_{c}}+\Delta {{L}_{s}}=1mm+0.25mm=1.25mm\]


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