Which of the following is true about moment of inertia (I) ?

I

about an axis is minimum, then it must pass through centre of mass

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Moments of Inertia about all axes passing through the centre of mass have same

I

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Perpendicular axis theorem can't be applied for 3 dimensional body

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Parallel axis theorem can be applied for 3 dimensional body

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Solution

The correct options are
A If $I$ about an axis is minimum, then it must pass through centre of mass
B Perpendicular axis theorem can't be applied for 3 dimensional body
C Parallel axis theorem can be applied for 3 dimensional body
(A) If $I$ about an axis is minimum, then $I$ about any other axis parallel to the axis passing through the center of mass is more which can verified from the parallel axis theorem. Hence, it must pass through centre of mass.
(B) Moment of Inertia about all axis passing through centre of mass have same $I$ is not correct.
(C) Perpendicular axis theorem can be applied to laminar bodies only
(D) Parallel axis theorem can be applied to 3D bodies, it is an general expression

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