KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    A rod of length 1000 mm and co-efficient of linear expansion \[a={{10}^{-4}}\] per degree is placed symmetrically between fixed walls separated by 1001 mm. The Young's modulus of the rod is \[{{10}^{11}}\text{ }N/{{m}^{2}}\]. If the temperature is increased by \[20{}^\circ C\,\], then the stress developed in the rod is (in\[N/{{m}^{2}}\]):

    A) 10              

    B) \[{{10}^{8}}\]

    C) \[2\times {{10}^{8}}\]

    D) cannot be calculated

    Correct Answer: B

    Solution :

    The change in length of rod due to increase in temperature in absence of walls is
    \[\Delta \ell =\ell \alpha \Delta T\]\[=1000\times {{10}^{-4}}\times 20\,mm\]\[=2\,mm\]
    But the rod can expend upto 1001 mm only.
    At that temperature its natural length is = 1002 mm.
    \[\therefore \] compression = 1 mm
    \[\therefore \] mechanical stress = \[Y\frac{\Delta \ell }{\ell }={{10}^{11}}\times \frac{1}{1000}\]

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