Let IA and IB be moment of inertia of a body about two axis...

Let $I_{A}$ and $I_{B}$ be moment of inertia of a body about two axis $A$ and $B$ respectively. The axis of body $A$ passes through the centre of mass of the body but $B$ does not. Then : (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 $I_{A}>I_{B}$

Let $I_{A}$ and $I_{B}$ be moment of inertia of a body about two axis $A$ and $B$ respectively. The axis of body $A$ passes through the centre of mass of the body but $B$ does not. Then :
(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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Key Concepts

Centre of Mass

The centre of mass is the point where the total mass of a body can be considered to be concentrated. It is a critical point in dynamics when calculating motion, especially for rotational motion, as rotations about this point often simplify analysis.

Parallel Axis Theorem

This theorem provides a method to compute the moment of inertia of an object about any axis parallel to an axis through its centre of mass. It states that the moment of inertia about the parallel axis equals the moment of inertia about the centre of mass plus the product of the mass of the object and the square of the distance between the two axes.

Moment of Inertia

This concept quantifies an object's resistance to angular acceleration about a given axis. It depends on the mass distribution relative to the axis, such that if mass elements are located farther from the axis, the moment of inertia increases.

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