NEET 2002 Physics 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 :

(1)Aluminium at interior and iron surround to itCorrect
(2)Iron at interior and aluminium surround to it
(3)Using iron and aluminium layers in alternate order
(4)Sheet of iron is used at both external surface and aluminium sheet as internal layers

Answer: (1)

Solution

Moment of inertia about the geometrical axis is , so mass placed farther from the axis contributes much more. For a fixed total size and fixed amounts of material, is maximum when the denser material is kept at the largest radii. Iron is denser than aluminium ($ρ_{Fe} ≈ 7.8\

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Question ID VK-088937