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

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B

iron at interior and aluminum surround to it

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C

using iron and aluminum layers in alternate order

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D

sheet of iron is used at both external surface and aluminum sheet as internal layers

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Solution

## The correct option is A aluminum at the interior and iron surround to itExplanation :A circular disc is divided into a large number of circular rings.The moment of inertia (MOI) of a circular ring is a summation of all the rings MOI of circular ring =$M{R}^{2}$, here $M$ is the mass and $R$is the radius of the ring Density =$\frac{mass}{volume}$The density of iron is more than aluminum, therefore for same volume mass will be more for iron.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

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