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DUMET Medical DUMET Medical Solved Paper-2010

  • question_answer
    Two stars of masses m, and m2 are part of a binary star system. The radii of their orbits are \[{{r}_{1}}\]and \[{{r}_{2}}\] respectively, measured from the CM of the system. The magnitude of acceleration of \[{{m}_{1}}\] is   

    A)  \[\frac{{{m}_{1}}{{m}_{2}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    B)  \[\frac{{{m}_{1}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    C)  \[\frac{{{m}_{2}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    D)  \[\frac{{{m}_{1}}+{{m}_{2}}}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    Correct Answer: C

    Solution :

     The distance between the centres of the two stars \[=({{r}_{1}}+{{r}_{2}})\] The force acting between the stars is given by \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}={{m}_{1}}{{a}_{{{m}_{1}}}}\] Hence, the acceleration of mass \[{{m}_{1}}\] \[{{a}_{{{m}_{1}}}}=\frac{G{{m}_{2}}}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]


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