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 ratio 3:5. The moments of inertia of these discs about their diameters are in the ratio x/6. The value of x is ______.
Physics · Circular Motion
JEE Mains 31 January 2023 Shift 2 Evening Shift

Question

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 ratio 3:5. The moments of inertia of these discs about their diameters are in the ratio x/6. The value of x is ______.

Physics · Circular Motion

JEE Mains 31 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

For equal masses M = ρπR²t, so R₁²/R₂² = ρ₂t₂/(ρ₁t₁) = (5×0.5)/(3×1) = 5/6. Moment of inertia of a thin disc about a diameter is (1/4)MR². Since masses are equal, I₁/I₂ = R₁²/R₂² = 5/6. Hence x=5.