Question

A circular disc is to be made by using iron and aluminium, so that it acquires maximum moment of inertia about its geometrical axis, it is possible with
A) Iron and aluminium layers in alternate order
B) Aluminium at interior and iron surrounding it
C) iron at interior and aluminium surrounding it
D) Either (A) or (C)

Answer 1

Moment of inertia is the product of mass and square of the distance from the centre. Here we have to apply the same concept if the body has made a combination of different materials.

Complete step by step answer:
Circular disc means it is made up of a number of concentric rings. Here it is mentioned that it is made of aluminium and iron rings. In order to attain maximum moment of inertia for the circular disc we have to find the correct order of these circular rings among the given options.
Since a circular disc consists of a number of circular rings, the moment of inertia of the disc is the summation of the moment of inertia of the circular rings about its geometric axis.
The moment of inertia of the body is given by $I={\rm mr}^2$ ---- (i)
Where I is the moment of inertia, m is the mass of the body and r is the distance from the centre of the circular rings.
Since it is made up of aluminium and iron, we compare corresponding densities. Density is the ratio of mass to unit volume. The density of iron is more than that of aluminium. Density is directly proportional to the mass which in turn density is directly proportional to the moment of inertia. Moment of inertia is also directly proportional to radius of the circular path. Hence the circular ring made of iron to be placed at a higher radius to have more value of moment of inertia. Hence, we conclude that to get maximum value of moment of inertia for the circular disc, we have to place aluminium at the interior and iron at the outer part.
Hence, option B is the correct answer.

Note: To get the higher value of moment of inertia it has to be placed in such a way that the mass density should be more in the outer part of the disc.