Two discs have radii 0.1 m and 0.4 m. Their moment of inertia about their axes will be in the ratio of (assume same thickness and material)

Question

Two discs have radii 0.1 m and 0.4 m. Their moment of inertia about their axes will be in the ratio of (assume same thickness and material) (A) 1: 144 (B) 1: 225 (C) 1: 256 (D) 1: 169

Tardigrade Admin · Accepted Answer

I: (1/2) M R2, m = v × ρ = A × t × ρ=π R 2 × t × ρ ∴ I=(1/2)(π R2 × t × ρ) R2 propto R4 ∴ I propto R4 ⇒ (I1/I2)=((R1/R2))4 =((0.1/0.4))4=(1/256)

Q. Two discs have radii $0.1 m$ and $0.4 m$ . Their moment of inertia about their axes will be in the ratio of (assume same thickness and material)

$1 : 144$

$1 : 225$

$1 : 256$

$1 : 169$

$I : \frac{1}{2} M R^{2}, m = v \times ρ$
$= A \times t \times ρ = π R^{2} \times t \times ρ$
$∴ I = \frac{1}{2} (π R^{2} \times t \times ρ) R^{2} \propto R^{4}$
$∴ I \propto R^{4}$
$\Rightarrow \frac{I _{1}}{I _{2}} = (\frac{R _{1}}{R _{2}})^{4}$
$= (\frac{0.1}{0.4})^{4} = \frac{1}{256}$

Q. Two discs have radii 0.1m and 0.4m. Their moment of inertia about their axes will be in the ratio of (assume same thickness and material)

1:144

1:225

1:256

1:169