A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r

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A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia IA and IB is

(a) IA >IB

(b) IA =IB

(c) IA B

(d) depends on the actual values of t and r.


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Salim Ahmed Kawsar

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(c) IA <IB  

Explanation: 

Let the density of iron plate be ρ. 

Mass of first disc m = πr²tρ 

M.I. = IA = ½mr² == ½πr²tρr² = ½πr4tρ 

Mass of second disc = M = π(4r)²(t/4)ρ = 4πr²tρ 

M.I. = IB = ½M(4r)² = ½4πr²tρ16r² = 32πr4tρ 

Clearly, IA < IB.

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