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Question

A circular disc X of radius 'R' is made from an iron plate of thickness 't', and another disc Y of radius '4R' is made from an iron plate of thickness 't4'. Then the relation between the moment of inertia Ix and Iy is

A
Iy=64Ix
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B
Iy=32Ix
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C
Iy=16Ix
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D
Iy=Ix
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Solution

The correct option is A Iy=64Ix
Moment of Inertia of disc I=12MR2=12(πR2tρ)R2=12πtρR4
[As M=V×ρ=πR2tρ where t = thickness, ρ = density]
IyIx=tytx(RyRx)4 [ If ρ = constant]
IyIx=14(4)4=64 [Given Ry=4Rx,ty=tx4]
Iy=64Ix

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