A uniform solid cylinder has radius R and length L with moment of inertia I₁ about its axis. A concentric cylinder of radius R/2 and length L/2 is carved out. If I₂ is the moment of inertia of the carved-out part about the same axis, find I₁/I₂.
Physics · Rotational Motion · moment of inertia and kinetic energy in pure rotation
JEE Mains 2023

Question

A uniform solid cylinder has radius R and length L with moment of inertia I₁ about its axis. A concentric cylinder of radius R/2 and length L/2 is carved out. If I₂ is the moment of inertia of the carved-out part about the same axis, find I₁/I₂.

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

JEE Mains 2023

G1 Physics · Accepted Answer

For the original cylinder I₁ = ½MR². The carved cylinder has radius R/2, length L/2 and hence mass M/8. Thus I₂ = ½(M/8)(R/2)² = MR²/64. Therefore I₁/I₂ = 32.