Question

Moment of inertia of a ring of mass $M$ and radius $R$ about an axis passing through the centre and perpendicular to the plane is $I$. What is the moment of inertia about its diameter?

• A. $I$
• B. $\frac{I}{2}$
• C. $\frac{I}{\sqrt{2}}$
• D. $I+{MR}^2$

Answer 1

The correct option is B $\frac{I}{2}$

By using perpendicular axis theorem,

$I_{zz}=I_{xx}+I_{yy}$

about diameter so $I_{xx}=I_{yy}$

so $I_{zz}=2Ixx$

so moment of inertia about diameter $I_{xx}=\frac{I_{zz}}{2}$

so let moment of inertia about z axis be I

in that case answer will be I/2.