2002 AIPMT System of Particles and Rotational MotionMoment of Inertia Easy Question 8 of 8 in Moment of Inertia

A circular disc is to be made by using iron and aluminium so that it acquires 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

The answer is A.

Solution

Moment of inertia: $I = \sum mr^2$. Mass placed farther from the axis contributes much more, since it is multiplied by $r^2$.
The density of iron (about 7.8 g/cm$^3$) is more than that of aluminium (about 2.7 g/cm$^3$).
So to make I maximum, the heavier material (iron) should be placed far from the axis, i.e. on the outer ring, and the lighter aluminium in the interior.
Putting iron sheets on the two flat faces does not move mass farther from the axis.
So the moment of inertia is maximum with aluminium at the interior and iron surrounding it.

Concept Distribution of mass and moment of inertia

Moment of Inertia in past papers

8 questions from this chapter have appeared across 7 exam years.