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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    The density of a non-uniform rod of length 1 m is given by \[\rho (x)=a(1+b{{x}^{2}})\] where a and b are constants and 0 \[\le \] x \[\le \] 1. The centre of mass of the rod will be

    A)  \[\frac{3\,(2+b)}{4\,(3+b)}\]                     

    B)  \[\frac{4\,(2+b)}{3\,(3+b)}\]

    C)  \[\frac{3\,(2+b)}{4\,(2+b)}\]                     

    D)  \[\frac{4\,(3+b)}{3\,(2+b)}\]

    E)  \[\frac{2\,(3+b)}{3\,(6+b)}\]

    Correct Answer: A

    Solution :

                    Here \[\rho (x)=a\,(1+b{{x}^{2}})\] When \[b\to 0\,(x)=a\]constant i.e. density of rod of length 1m is constant. In that event centre of mass of rod would lie at 0.5m (i.e. at the cutre of rod). When are try \[b\to 0\] in all the four given option, we find choice  alone given \[x=\frac{3\,(2+b)}{4\,(3+b)}\]    \[=\frac{6}{12}=0.5\]


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