Question

A circular disc is to be made by using iron and aluminum so that it acquired maximum moment of inertia about geometrical axis. It is possible if

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

Answer 1

The correct option is A

aluminum at the interior and iron surround to it

Explanation :

1. A circular disc is divided into a large number of circular rings.
2. The moment of inertia (MOI) of a circular ring is a summation of all the rings
3. MOI of circular ring =$M{R}^2$, here $M$ is the mass and $R$is the radius of the ring
4. Density =$\frac{mass}{volume}$
5. The density of iron is more than aluminum, therefore for same volume mass will be more for iron.
6. To get the maximum value of $M{R}^2$, more mass has to be concentrated on outside. Therefore, iron must be placed in the exterior and aluminum in the interior. i.e., Aluminum should be placed at a greater radius

Hence, to get a maximum moment of inertia for the circular disc, aluminum should be placed in the interior whereas iron must be surrounded outside.

Therefore option A is correct