Question

The moment of inertia of a circular disc of radius 2 m and mass 1 kg about an axis XY passing through its centre of mass and perpendicular to the plane of the disc is 2 kg m\(^2\). The moment of inertia about an axis parallel to the axis XY and passing through the edge of the disc is

• A. 6 kg m\(^2\)
• B. 4 kg m\(^2\)
• C. 10 kg m\(^2\)
• D. 8 kg m\(^2\)

Hint:

The parallel axis theorem is invaluable for shifting axes. The distance \(d\) is the perpendicular separation between the two axes. For a disc, the centre‑to‑edge distance is exactly its radius.

Answer 1

The Correct Option is A

Step 1: Use the parallel axis theorem.
Moving the axis by a distance $d$ adds $Md^2$: $I = I_{cm} + Md^2$.

Step 2: Find the shift distance.
The edge axis is one radius away from the centre, so $d = R = 2\ \text{m}$.

Step 3: Substitute.
With $I_{cm} = 2$, $M = 1$: \[ I = 2 + (1)(2)^2 = 2 + 4. \]

Step 4: Add.
\[ \boxed{6\ \text{kg m}^2} \]