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BVP Medical BVP Medical Solved Paper-2001

  • question_answer
    Two rods of different materials having coefficients of the thermal expansion \[{{\alpha }_{1}},{{\alpha }_{2}}\]and Youngs moduli,\[{{\gamma }_{1}},{{\gamma }_{2}}\] 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 the rods. If \[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\]. The thermal, stresses developed in the two rods are equal provided, \[{{\gamma }_{1}}:{{\gamma }_{2}}\]is equal to :

    A)  5 : 3                                      

    B)  1 : 2

    C)  9 : 4                                      

    D)  3 : 2

    Correct Answer: D

    Solution :

                  Suppose l is the original length of the rod. Suppose these are heated up to \[{{t}^{o}}C\]. Now, increase in length \[=\alpha lt\] Where a is the coefficient of linear expansion of the rod. Now,  strain \[=\alpha lt/l=\alpha t\] We know that Stress = Y \[\times \] strain = \[Y\alpha t\] According to question, stresses are equal for the two rods if \[{{Y}_{1}}{{\alpha }_{1}}t={{Y}_{2}}{{\alpha }_{2}}t\] or  \[\frac{{{Y}_{1}}}{{{Y}_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}=\frac{3}{2}\]


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