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JEE Main & Advanced JEE Main Paper (Held On 10-Jan-2019 Evening)

  • question_answer
    Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

    A) \[\frac{17}{15}M{{R}^{2}}\]               

    B) \[\frac{137}{15}M{{R}^{2}}\]

    C) \[\frac{209}{15}M{{R}^{2}}\]

    D)                  \[\frac{152}{15}M{{R}^{2}}\]

    Correct Answer: A

    Solution :

    \[I=2{{I}_{sp}}+{{I}_{rod}}\] \[=2\left[ \frac{2}{5}M{{R}^{2}}+M{{(2R)}^{2}} \right]+\frac{M{{(2R)}^{2}}}{12}\] \[=\,\,\,2\left[ \frac{22}{5}M{{R}^{2}} \right]+\frac{M{{R}^{2}}}{3}\] \[=\,\,\,\frac{(132+5)}{15}M{{R}^{2}}\] \[I=\frac{137}{15}M{{R}^{2}}\]         


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