Question

A composite disc is to be made using equal masses of aluminum and iron so that it has as high a moment of inertia as possible. This is possible when

• A. The surfaces of the discs are made of iron with aluminum inside
• B. The whole of aluminum is kept in the core and the iron at the outer rim of the disc
• C. The whole of the iron is kept in the core and the aluminum at the outer rim of the disc
• D. The whole disc is made with thin alternate sheets of iron and aluminum

Answer 1

The correct option is B

The whole of aluminum is kept in the core and the iron at the outer rim of the disc

The correct option is (B) The whole of aluminum is kept in the core and the iron at the outer rim of the disc

We know,

The density of iron > Density of aluminum

Moment of inertia is given by the formula

$I=\int r^{2}dm$

Where r is the distance of the mass from the axis and $dm$ is the small mass

From the formula, we can say that the moment of inertia will be greater if the mass will be greater

As we have already discussed the density of iron is greater than the density of aluminum so if the volume of the iron will also be high then the total mass will be high and the moment of inertia will be maximum

So,

${\rho }_{iron}>{\rho }_{aluminum}$

And hence aluminum should be kept at the core and iron should be placed at the outer part to make the moment of inertia maximum.