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Punjab Medical Punjab - MET Solved Paper-2008

  • question_answer
    Two rods of different materials with coefficients of linear thermal expansion\[{{\alpha }_{1}},\,\,{{\alpha }_{2}}\]and Youngs moduli \[{{Y}_{1}}\] and \[{{Y}_{2}}\] respectively are fixed between two rigid walls. They are heated to have the same increase in temperature. If the rods do not bend and if\[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\], then the thermal stresses developed in the two rods will be equal when \[{{Y}_{1}}:{{Y}_{2}}\] is equal to

    A) \[2:3\]                                  

    B) \[2:5\]

    C) \[3:2\]                                  

    D) \[5:2\]

    Correct Answer: C

    Solution :

    Thermal stress \[=Y\times \] strain or            \[S=Y\varepsilon \] or            \[S=Y\,\,\alpha \,\,t\] where \[\alpha =\]linear thermal expansion \[Y=\] Youngs modulus Here,         \[{{S}_{1}}={{S}_{2}}\] \[\Rightarrow \]               \[{{Y}_{1}}{{\alpha }_{1}}t={{Y}_{2}}{{\alpha }_{2}}t\] or               \[\frac{{{Y}_{1}}}{{{Y}_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}=\frac{3}{2}\] Thus,  \[{{Y}_{1}}:{{Y}_{2}}=3:2\]


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