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Moment of Inertia of a Rod

Let IA and IB...

Question

Let I_A and I_B be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not.
(a) I_A < I_B
(b) If I_A < I_B, the axes are parallel
(c) If the axes are parallel, I_A < I_B
(d) If the axes are not parallel, I_A ≥ I_B.

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Solution

(c) If the axes are parallel, I_A < I_B

If axes A and B are parallel, we get:
_{$I_{B} = I_{A} + m r^{2}$}
Here, r is the distance between two axes and m is the mass of the body.
$∴$ I_A < I_B

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