Two discs of same mass and same thickness (t) are made from two different materials of densities ' d₁ ' and ' d₂ ' respectively. The ratio of the moment of inertia I₁ to I₂ of two discs about an axis passing through the centre and perpendicular to the plane of disc is (a) d₁: d₂ (b) d₂: d₁ (c) 1: d₁ d₂ (d) 1: d₁² d₂

Answer: (b). Same mass and thickness: M = π R² t d ⇒ R² ∝ 1/d. I = MR²/2 ∝ R² ∝ 1/d (I₁)/(I₂) = (d₂)/(d₁) So the answer is (b) d₂: d₁.

Two discs of same mass and same thickness (t) are made from two… | MHT CET 2023 (9 May, Shift 1)

Q105MHT CET 2023 · 9 MAY · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Two discs of same mass and same thickness (t) are made from two different materials of densities ' $d_1$ ' and ' $d_2$ ' respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is

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Answer: (b)

Same mass and thickness: $M = \pi R^2 t d \Rightarrow R^2 \propto \frac{1}{d}$ .
$I = \frac{MR^2}{2} \propto R^2 \propto \frac{1}{d}$
$\frac{I_1}{I_2} = \frac{d_2}{d_1}$
So the answer is (b) $d_2 : d_1$ .

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Moment of Inertia & Radius of Gyration question from MHT CET 2023 (9 May, Shift 1)

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