Two rings of radius R and n R made up of same material have the ratio of moment of inertia about an axis passing through the centre as 1 : 8 . The value of n is

Question

Two rings of radius R and n R made up of same material have the ratio of moment of inertia about an axis passing through the centre as 1 : 8 . The value of n is, 2, 2 2, 4, 1 2

MARKS App · Accepted Answer

The ratio of moment of inertia of the rings I 1 I 2 = M 1 M 2 R 1 R 2 2 = λ l 1 λ l 2 R 1 R 2 2 = 2 π R 2 π nR R nR 2 λ = linear density of wire = constant ⇒ I 1 I 2 = 1 n 3 = 1 8 given ∴ n 3 = 8 ⇒ n = 2

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