Maximum Moment of Inertia for Composite Disc – Rankers Physics

Moment of Inertia: Practice Problem & Solution

A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with: (2002)
Aluminium at interior and iron surround to it.
Iron at interior and aluminum surround to it.
Using iron and aluminium layers in alternate order.
Sheet of iron is used at both external surface and aluminium sheet as internal layers.

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:

Moment of inertia is $I = \int r^2 dm$. To maximize $I$, denser material (iron) should be placed at the outer periphery and lighter material (aluminium) at the interior.

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