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 . The value of is _ _ _ _ .

Step-by-step solution

For a circular disc made of material with density , moment of inertia is I = 1 2 MR^2 = 1 2 R^2 T R^2 = 1 2 R^4 T . For disc 1: I₁ = 1 2 R₁^4 T₁ For disc 2: I₂ = 1 2 R₂^4 T₂ Given I₁ = I₂ : R₁^4 T₁ = R₂^4 T₂ With R₁ R₂ = 2 : (2R₂)^4 T₁ = R₂^4 T₂ 16 R₂^4 T₁ = R₂^4 T₂ T₁ T₂ = 1 16 Therefore = 16 .