Question
GeneralGeneralGeneral

Two discs have the same moment of inertia about their axis. Thicknesses are t₁ and t₂, densities are same, and R₁/R₂ = 1/4. Find t₁/t₂.

Verified Answer

For a disc,

I = 1/2 MR²

Mass of disc:

M = ρπR²t

So,

I = 1/2 (ρπR²t)R²

I ∝ tR⁴

Since both discs have same moment of inertia,

t₁R₁⁴ = t₂R₂⁴

Given:

R₁/R₂ = 1/4

Therefore,

t₁/t₂ = (R₂/R₁)⁴

= 4⁴ = 256

Answer:

t₁/t₂ = 256