A uniform solid cylinder with radius R and length L has moment of inertia I₁, about the axis of cylinder. A concentric solid cylinder of radius R' = R/2 and length L' = L/2 is caned out of the original cylinder. If I₂ is the moment of inertia of the carved out portion of the cylinder then I₁/I₂ = __________ (Both I₁ and I₂ are about the axis of the cylinder)
Physics · Rotational Motion · moment of inertia and kinetic energy in pure rotation
JEE Mains 24 January 2023 Shift 2 Evening Shift

Question

A uniform solid cylinder with radius R and length L has moment of inertia I₁, about the axis of cylinder. A concentric solid cylinder of radius R' = R/2 and length L' = L/2 is caned out of the original cylinder. If I₂ is the moment of inertia of the carved out portion of the cylinder then I₁/I₂ = __________ (Both I₁ and I₂ are about the axis of the cylinder)

Physics · Rotational Motion · moment of inertia and kinetic energy in pure rotation

JEE Mains 24 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

For a solid cylinder, I = (1/2)MR². The smaller cylinder has radius R/2 and length L/2, so its mass is proportional to R'²L' = (R²/4)(L/2), giving M₂ = M₁/8. Therefore I₂ = (1/2)(M₁/8)(R/2)² = M₁R²/64, while I₁ = M₁R²/2. Hence I₁/I₂ = 32.