Question

Two disc of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1 : 3. The moment of inertia of these disc about the respective axes passing through their centres and perpendicular to their planes will be in the ratio. 

(A) 1 : 3 

(B) 3 : 1 

(C) 1 : 9 

(D) 9 : 1

Answer 1

Correct option: (B) 3 : 1

Explanation:

Given : thickness = t₁ = t₂ 

masses = m₁ = m₂ 

density (ρ₁ / ρ_2­) = (1/3)

I = MI of disc = [(MR²) / 2]          (1)

also ρ = [(mass) / (volume)]

= [(mass) / (area × thickness)]

= [m / (πR²t)]

R² = [m / (πtρ)]

from (1)

I = (M/2)R² 

= (M/2) ∙ [M / (πtρ)]

= [M² / (2πTρ)]

given: thickness & masses same.

hence l ∝ (1/p)

(I₁ / I₂) = (ρ₂ / ρ₁) as t₁ = t₂ m₁ = m₂ 

(I₁ / I₂) = (3/1)