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  4. Moment of inertia of ring about its diameter is I. Then, moment of inertia about an axis passing through centre perpendicular to its plane is

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Q. Moment of inertia of ring about its diameter is I. Then, moment of inertia about an axis passing through centre perpendicular to its plane is

System of Particles and Rotational Motion

Solution:

From perpendicular axis theorem we have,
$
I_{2}=I_{x}+I_{y}
$
Given, $I_{2}=I$ and about diameter $I=Z_{y}=I^{\prime}$
$
\therefore \quad I=I^{\prime}+I^{\prime} \\
I=2 I^{\prime} \\
I^{\prime}=\frac{I}{2}
$