Rotational Motion

JEE Main level, single correct, medium

85 of 280

Question 85 of 280

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:

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Answer: (A) 1812MR2\dfrac{181}{2}M{R}^{2}

The motion of inertia of the system about OO,

12MR2+6×12MR2+6×M×(2R)2\dfrac{1}{2}M{R}^{2}+6\times \dfrac{1}{2}M{R}^{2}+6\times M\times {\left(2R\right)}^{2}

⇒I1=72MR2+24MR2\Rightarrow {I}_{1}=\dfrac{7}{2}M{R}^{2}+24M{R}^{2}

The motion of inertia of the system about PP,

⇒I1+7MD2{\Rightarrow I}_{1}+7M{D}^{2}

⇒72MR2+24MR2+7M×(3R)2\Rightarrow \dfrac{7}{2}M{R}^{2}+24M{R}^{2}+7M\times {\left(3R\right)}^{2}

⇒1812MR2\Rightarrow \dfrac{181}{2}M{R}^{2}

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