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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 it


Explanation :

  1. A circular disc is divided into a large number of circular rings.
  2. The moment of inertia (MOI) of a circular ring is a summation of all the rings
  3. MOI of circular ring =MR2, here M is the mass and Ris the radius of the ring
  4. Density =massvolume
  5. The density of iron is more than aluminum, therefore for same volume mass will be more for iron.
  6. To get the maximum value of MR2, 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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