JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

  • question_answer
    Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: [JEE Main Online 08-04-2018]

    A)  \[\frac{\text{73}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}\]                 

    B)  \[\frac{\text{181}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}\]

    C)  \[\frac{\text{19}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}\]                 

    D)  \[\frac{\text{55}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}\]

    Correct Answer: B

    Solution :

    \[I=\left( \frac{M{{R}^{2}}}{2} \right)+6\left[ \frac{M{{R}^{2}}}{2}+M{{(2R)}^{2}} \right]=\frac{M{{R}^{2}}}{2}+6\left[ 4.5\,\,M{{R}^{2}} \right]\] \[I=27.5\,\,M{{R}^{2}}=\frac{55}{2}M{{R}^{2}};{{I}_{P}}=\frac{55}{2}M{{R}^{2}}+(7M){{(3R)}^{2}}=\frac{181M{{R}^{2}}}{2}\]


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