Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0 . 5 cm respectively. The densities of materials are in the ratio 3 : 5 . The moment of inertia of these discs respectively about their diameters will be in the ratio of x 6 . The value of x is ______.

Step-by-step solution

Mass of the disc in terms of density can be written as, m = ρ π R 2 t . ⇒ R 2 = m ρ π t Now moment of inertia of the disc about the diameter is, m R 2 4 . Therefore, I = m R 2 4 = m 2 4 ρ π t ⇒ I ∝ 1 ρ t Required ratio, I 1 I 2 = ρ 2 t 2 ρ 1 t 1 = 5 3 × 0 . 5 1 = 5 6 Hence, x = 5 .