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JEE Main & Advanced Physics Elasticity Question Bank Critical Thinking

  • question_answer
    Two rods of different materials having coefficients of linear expansion \[{{\alpha }_{1}},\,{{\alpha }_{2}}\] and Young's moduli \[{{Y}_{1}}\] and \[{{Y}_{2}}\] respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If \[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\], the thermal stresses developed in the two rods are equally provided \[{{Y}_{1}}:{{Y}_{2}}\] is equal to                         [IIT 1989]

    A) 2 : 3    

    B)             1 : 1

    C)             3 : 2    

    D)             4 : 9

    Correct Answer: C

    Solution :

    Thermal stress = \[Y\alpha \Delta \theta \]. If thermal stress and rise in temperature are equal then \[Y\propto \frac{1}{\alpha }\] Þ \[\frac{{{Y}_{1}}}{{{Y}_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}=\frac{3}{2}\]


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