About which axis will the moment of inertia o | vedclass

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(D) Let the mass of the ring be $M$ and radius be $R$. $1$. Moment of inertia $(I)$ about an axis passing through the center and perpendicular to the

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Tangent to the ring and perpendicular to the plane of the ring

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(D) Let the mass of the ring be $M$ and radius be $R$. $1$. Moment of inertia $(I)$ about an axis passing through the center and perpendicular to the plane: $I_z = MR^2$. $2$. Moment of inertia about a diameter $(I_d)$: By the perpendicular axis theorem,$I_x + I_y = I_z$. Since $I_x = I_y = I_d$,we have $2I_d = MR^2$,so $I_d = \frac{1}{2}MR^2$. $3$. Moment of inertia about a tangent in the plane $(I_t)$: By the parallel axis theorem,$I_t = I_d + MR^2 = \frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2$. $4$. Moment of inertia about a tangent perpendicular to the plane $(I_p)$: By the parallel axis theorem,$I_p = I_z + MR^2 = MR^2 + MR^2 = 2MR^2$. Comparing the values: $MR^2$,$0.5MR^2$,$1.5MR^2$,and $2MR^2$. The maximum value is $2MR^2$.

Column-$I$	Column-$II$
$(1)$ Moment of inertia of a solid sphere about its diameter	$(a)$ $\frac{2}{3}MR^2$
$(2)$ Moment of inertia of a solid sphere about a tangent	$(b)$ $\frac{2}{5}MR^2$
	$(c)$ $\frac{7}{5}MR^2$

About which axis will the moment of inertia of a ring be maximum?

Similar Questions

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Match the items in Column-$I$ with those in Column-$II$.
Column-$I$ Column-$II$
$(1)$ Moment of inertia of a solid sphere about its diameter $(a)$ $\frac{2}{3}MR^2$
$(2)$ Moment of inertia of a solid sphere about a tangent $(b)$ $\frac{2}{5}MR^2$
$(c)$ $\frac{7}{5}MR^2$

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