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

  • question_answer
    A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is\[2\times {{10}^{11}}N{{m}^{-2}}\]. The percentage strain is about

    A) 0.16%

    B) 0.32%

    C) 0.08%

    D) 0.24%43

    Correct Answer: A

    Solution :

    [a] Given: \[F=100kN={{10}^{5}}N\] \[Y=2\times {{10}^{11}}N{{m}^{-2}}\] \[{{\ell }_{0}}=1.0m\] radius \[r=10mm={{10}^{-2}}m\] \[From\,formula,\,Y=\frac{Stress}{strain}\] \[\Rightarrow Strain=\frac{Stress}{Y}=\frac{F}{AY}\] \[=\frac{{{10}^{5}}}{\pi {{r}^{2}}Y}=\frac{{{10}^{5}}}{3.14\times {{10}^{-4}}\times 2\times {{10}^{11}}}=\frac{1}{628}\] Therefore % strain \[=\frac{1}{628}\times 100=0.16%\]


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