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Question

# Find the moment of inertia of ring of mass M and radius R about the axis passing through the ring diametrically. If moment of inertia about the axis passing through its center of mass and perpendicular to the plane is MR2.

A
MR2
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B
2MR2
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C
MR24
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D
MR22
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Solution

## The correct option is D MR22Given, MOI of ring about the axis passing through the center of masss and perpendicular to its plane is Iz=MR2. Now, MOI of ring about the axis passing along its diameter is given by Ix or Iy Using perpendicular axis theorem we have Iz=Ix+Iy But, Ix=Iy, by symmetry ⇒ Ix=Iy=Iz2 ⇒ Ix=Iy=MR22

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