Moment of Inertia and Parallel Axis Theorem – Rankers Physics

Moment of Inertia: Practice Problem & Solution

Assertion (A): If two different axes are at same distance from the centre of mass of a rigid body then moment of inertia of the given rigid body about both the axes will always be equal. Reason (R): According to perpendicular axis theorem \(\text{I} = \text{I}_{\text{cm}} + \text{Md}^2\) where symbols have their usual meaning.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Moment of Inertia. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is false. Moment of inertia depends on both the distance and the orientation of the axis. Reason (R) is false. The given formula is for the parallel axis theorem, not the perpendicular axis theorem.

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