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  4. Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

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Q. Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

Rajasthan PMTRajasthan PMT 2002System of Particles and Rotational Motion

Solution:

Moment of inèrtia of ring $I=m r^{2}$.
image
Moment of inertia of ring about diameter
(from theorem of parallel axis)
$I_{1} =m r^{2}+m r^{2}=2 m r^{2} $
$I: I_{2} =1: 2$