Three rings each of mass M and radius R are a | vedclass

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(B) The axis $YY'$ passes through the center of the top ring and is a diameter of that ring. The moment of inertia of the top ring about its diameter

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$\frac{7}{2} MR^2$

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(B) The axis $YY'$ passes through the center of the top ring and is a diameter of that ring. The moment of inertia of the top ring about its diameter is $I_1 = \frac{1}{2} MR^2$.For the two lower rings,the axis $YY'$ is a tangent to each ring in its own plane. According to the parallel axis theorem,the moment of inertia of a ring about a tangent in its plane is $I_{tangent} = I_{cm} + MR^2 = \frac{1}{2} MR^2 + MR^2 = \frac{3}{2} MR^2$.Since there are two such lower rings,their combined moment of inertia is $I_2 + I_3 = \frac{3}{2} MR^2 + \frac{3}{2} MR^2 = 3 MR^2$.The total moment of inertia of the system about the axis $YY'$ is $I = I_1 + I_2 + I_3 = \frac{1}{2} MR^2 + \frac{3}{2} MR^2 + \frac{3}{2} MR^2 = \frac{7}{2} MR^2$.

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis $YY'$ will be

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