Two discs of same mass and thickness are made of materials having different densities. Which one of them will having different densities. Which one of them will have larger moment of inertia?

 Answer: The mass of the two discs is the same, that is, m1=m2. Therefore, V1 ρ1 = V2ρ2

(πr1^2)t.ρ1 = (πr2^2)t.ρ2

ρ1/ρ2 = r1^2/r2^2                                                   (i)

The ratio of moment of inertia of the two discs is given by 

I1/I2 = ((1/2)m1r1^2) / ((1/2)m2r2^2)

        = r1^2/r2^2                                                     (ii)

(as m1=m2)

Using Eqs. (i) and (ii), we have I1/I2 = ρ2/ρ1

Therefore, I ∝ 1/ρ

Hence, we conclude that the moment of inertia and density are inversely related to each other and the disc of material with lower density has the larger moment of inertia