A circular disc A of radius r is made from an iron plate of thickness t,
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 1/4. The relation between the moments of inertia IA and IB is
(a) lA > IB
(b) IA = IB
(c)IA
(d) depends on the actual values of t and r.
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(c) IA
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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