Question

Let IA and IB 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) IA < IB
(b) If IA < IB, the axes are parallel
(c) If the axes are parallel, IA < IB
(d) If the axes are not parallel, IA ≥ IB.

Answer 1

The axis A passes through the centre of mass of the body but B does not because, if the axes are parallel, IA < IB.

Explanation:

Well choice (c) is the correct answer, because we use the formula if the axes are parallel :      

                            $I_{0}=I_{c m}+m d^{2}$      

Theorem of parallel calculation axis-inertia moments.

The moment of inertia for rotations around an axis O is located at a distance D from the center of mass of the object is determined by :

                           $\mathrm{I}_{0}=\mathrm{I}_{500}+\mathrm{md}^{2}$

Where,

• $I_{c m}$ is the moment of rotational inertia around an axis parallel to O that passes through the center of mass.
• M is the rigid object's total mass.

The distance between the origin and the axis that passes through C.O.M is 0 for the first body .      

Therefore,      

                             $\mathrm{I}_{\mathrm{o}}=\mathrm{I}_{\mathrm{cm}}+\mathrm{m}(\mathrm{O})^{2}=\mathrm{I}_{\mathrm{cm}}$

Because in question, where the second body does not move through the C.O.M, there is a gap between the axes, say 'd '

So,                         $\mathrm{I}_{\mathrm{o}}=\mathrm{I}_{\mathrm{sc}}+\mathrm{m} \mathrm{d}^{2}$

Hence, option (c) If the axes are parallel, IA < IB is the correct answer.