Two rings of same mass m and radius R are pla | vedclass

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(D) Let the two rings be $R_1$ and $R_2$. Let the axis of rotation be the diameter of ring $R_1$ and perpendicular to the plane of ring $R_2$.For ring

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$\frac{\sqrt{3} R}{2}$

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(D) Let the two rings be $R_1$ and $R_2$. Let the axis of rotation be the diameter of ring $R_1$ and perpendicular to the plane of ring $R_2$.For ring $R_1$,the moment of inertia about its diameter is $I_1 = \frac{1}{2} m R^2$.For ring $R_2$,the axis is perpendicular to its plane and passes through its centre,so its moment of inertia is $I_2 = m R^2$.The total moment of inertia of the system is $I = I_1 + I_2 = \frac{1}{2} m R^2 + m R^2 = \frac{3}{2} m R^2$.Let $k$ be the radius of gyration of the system. The total mass of the system is $M = m + m = 2m$.We know that $I = M k^2$,so $\frac{3}{2} m R^2 = (2m) k^2$.Solving for $k$: $k^2 = \frac{3}{4} R^2$,which gives $k = \frac{\sqrt{3}}{2} R$.

Two rings of same mass $m$ and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is ............

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