Two rings of the same radius and mass are pla | vedclass

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Question

(C) Let the two rings be Ring $1$ and Ring $2$. Let the axis of rotation be $XX^{\prime}$,which passes through the common centre and is perpendicular

Vedclass · Accepted Answer

$(3/2) mr^2$

Vedclass · Answer

(C) Let the two rings be Ring $1$ and Ring $2$. Let the axis of rotation be $XX^{\prime}$,which passes through the common centre and is perpendicular to the plane of Ring $1$.For Ring $1$,the axis $XX^{\prime}$ is perpendicular to its plane and passes through its centre. Therefore,its moment of inertia is $I_1 = mr^2$.For Ring $2$,the axis $XX^{\prime}$ lies in its plane and passes through its centre. Therefore,its moment of inertia is $I_2 = (1/2) mr^2$.The total moment of inertia of the system is $I = I_1 + I_2 = mr^2 + (1/2) mr^2 = (3/2) mr^2$.

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