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

Answer: (A)

A circular disc may be divided into a large number of circular rings. Moment of inertia of the disc will be the summation of the moments of inertia of these rings about the geometrical axis.
Now, moment of inertia of a circular ring about its geometrical axis is $M{R}^2$, where $M$ is the mass and $R$ is the radius of the ring.
Since the density (mass per unit volume) for iron is more than that of aluminium, the proposed rings made of iron should be placed at a higher radius to get more value of $M{R}^2$. Hence to get maximum moment of inertia for the circular disc, aluminium should be placed at interior and iron at the outside.