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EAMCET Medical EAMCET Medical Solved Paper-2003

  • question_answer
    One end of a thin uniform rod of length L and mass M1 is rivetted to the centre of a uniform circular disc of radius r and mass M2, so that both are coplanar. The centre of mass of the combination from the centre of the disc is: (Assume that the point of attachment is at the origin)

    A)  \[\frac{L({{M}_{1}}+{{M}_{2}})}{2{{M}_{1}}}\]                  

    B)  \[\frac{L{{M}_{1}}}{2({{M}_{1}}+{{M}_{2}})}\]

    C)  \[\frac{2({{M}_{1}}+{{M}_{2}})}{L{{M}_{1}}}\]                  

    D)  \[\frac{2L{{M}_{1}}}{({{M}_{1}}+{{M}_{2}})}\]

    Correct Answer: B

    Solution :

                     \[x\]co-ordinate of centre of mass \[{{x}_{CM}}=\frac{{{M}_{1}}{{x}_{1}}+{{M}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] We know that, centre of mass lies at the centre. So,    \[{{m}_{2}}=0\]and \[{{x}_{1}}=\frac{L}{2}\] So,          \[{{x}_{CM}}=\frac{{{m}_{1}}L+0\times {{x}_{2}}}{2({{M}_{1}}+{{M}_{2}})}=\frac{{{M}_{1}}L}{2({{M}_{1}}+{{M}_{2}})}\]


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