A circular disc has radius R₁ and thickness T₁. Another circular disc made of the same material has radius R₂ and thickness T₂. If the moment of inertia of both discs are same and R₁/R₂ = 2 then T₁/T₂ = 1/α. The value of α i s ____.
Physics · Rotational Motion · moment of inertia and kinetic energy in pure rotation
JEE Mains 2026 22 January Morning Shift

Question

A circular disc has radius R₁ and thickness T₁. Another circular disc made of the same material has radius R₂ and thickness T₂. If the moment of inertia of both discs are same and R₁/R₂ = 2 then T₁/T₂ = 1/α. The value of α i s ____.

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

JEE Mains 2026 22 January Morning Shift

G1 Physics · Accepted Answer

Both discs are made of the same material, so their density ρ is the same. Mass of a disc is m = ρπR²T. Moment of inertia about its central axis is I = (1/2)mR². Therefore, I = (1/2)(ρπR²T)R² = (1/2)ρπR⁴T. Since the two moments of inertia are equal, R₁⁴T₁ = R₂⁴T₂. Hence, T₁/T₂ = (R₂/R₁)⁴. Given, R₁/R₂ = 2, so R₂/R₁ = 1/2. Therefore, T₁/T₂ = (1/2)⁴ = 1/16. The question states T₁/T₂ = 1/α. Thus, α = 16. Hence the answer is 16.