A circular disc x of radius R is made from an iron plate of thickness t. and another disc Y of radius 4R is made from an iron plate of thickness t/4 then the rotation between the moment of inertia Ix and Iy is :
Answer & explanation
Correct answer: option 2
Disc x : radius = R ; thickness = t
Disc y : radius = 4R ; thickness = (t/4)
Moment of Inertia = [(MR2) / 2]
∴ (I1 / I2) = (M1 / M2) (R1 / R2)2 ... (1)
also mass = density × volume
M = ρ ∙ V
M = ρ ∙ πR2t
material is same hence density is same.
(M1 / M2) = (R1 / R2)2 ∙ (t1 / t2)
= [R / (4R)]2 ∙ [t / (t/4)]
= (1 / 16) × 4 = (1/4)
From (1) : (I1 / I2) = (1/4) × [R / (4R)]2
(I1 / I2) = (1/4) × (1 / 16) = (1 / 64)
i.e Iy = 64 Ix