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RAJASTHAN PMT Rajasthan - PMT Solved Paper-1996

  • question_answer
    Two solid sphere is each of mass M and radius R/2 are connected with a mass less rod of length 2R. The moment of inertia of the system about an axis through the centre of any sphere and perpendicular to the rod is:

    A) \[\frac{21}{5}M{{R}^{2}}\]                          

    B)        \[\frac{2}{5}M{{R}^{2}}\]                             

    C)        \[\frac{5}{2}M{{R}^{2}}\]                                             

    D)        \[\frac{5}{21}M{{R}^{2}}\]

    Correct Answer: A

    Solution :

    \[{{I}_{YY}}={{({{I}_{P}})}_{YY}}+{{({{I}_{Q}})}_{YY}}\] \[=\frac{2}{5}M{{\left( \frac{R}{2} \right)}^{2}}+\left\{ \frac{2}{5}M{{\left( \frac{R}{2} \right)}^{2}}+M\,{{(2R)}^{2}} \right\}\] \[=\frac{21}{5}M{{R}^{2}}\]


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