Question

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 :-

• A. aluminium at interior and iron surround to it
• B. iron at interior and aluminium surround to it
• C. using iron and aluminium layers in alternate order
• D. sheet of iron is used at both external surface and aluminium sheet as internal layers

Answer 1

The Correct Option is A

To determine the configuration of iron and aluminium that maximizes the moment of inertia of a circular disc about its geometrical axis, let's understand the physics behind the moment of inertia.

The moment of inertia I of a body depends on how the mass is distributed with respect to the axis of rotation. It is given by:

I = \int r^2 \, dm

where r is the distance from the axis, and dm is an infinitesimal element of mass.

Conceptual Background:

• The moment of inertia increases as more mass is distributed farther from the axis of rotation.
• Iron has a higher density than aluminium. Therefore, a layer of iron far from the axis will contribute more to the moment of inertia compared to aluminium.

Let's evaluate the given options:

1. Aluminium at interior and iron surround to it: This configuration places the denser iron farther from the center, maximizing the moment of inertia by concentrating more mass at larger distances from the axis.
2. Iron at interior and aluminium surround to it: Here, the denser iron is closer to the axis, which is suboptimal for maximizing the moment of inertia.
3. Using iron and aluminium layers in alternate order: This distribution is more complex but typically won't maximize the distance of the densest material from the axis effectively.
4. Sheet of iron is used at both external surfaces and aluminium sheet as internal layers: This also increases the distance of dense iron from the axis, similar to option 1, but adding complexity without improving significantly over option 1.

Therefore, the configuration with aluminium at interior and iron surround to it effectively distributes the mass to maximize the moment of inertia.

Conclusion: The best configuration for maximum moment of inertia is aluminium at interior and iron surround to it.