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(A) The system consists of one central disc and six outer discs. We need to find the moment of inertia of the six outer discs about an axis passing th

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$27 m R^2$

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(A) The system consists of one central disc and six outer discs. We need to find the moment of inertia of the six outer discs about an axis passing through the centre of the central disc and perpendicular to the plane.For each outer disc,the distance of its centre from the central axis is $d = 2R$.The moment of inertia of a single disc about its own central axis (normal to the plane) is $I_{cm} = \frac{1}{2} m R^2$.Using the parallel axis theorem,the moment of inertia of one outer disc about the central axis is:$I_{outer} = I_{cm} + m d^2 = \frac{1}{2} m R^2 + m(2R)^2 = \frac{1}{2} m R^2 + 4 m R^2 = \frac{9}{2} m R^2$.Since there are six such outer discs,the total moment of inertia is:$I_{total} = 6 	imes I_{outer} = 6 	imes \frac{9}{2} m R^2 = 27 m R^2$.

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