Question

Two disc of the same material and thickness have radii 0.2m and 0.6m. Their moments of inertia about their axes will be in the ratio

• A. 1 : 81
• B. 1 : 27
• C. 1 : 9
• D. 1 : 3

Answer 1

The correct option is D 1 : 9

The moment of inertia (MOI) of the disc about the centre of mass and perpendicular to its plane is given by,

$I_{disc}=\frac{M{R}^2}{2}$

$\Rightarrow I_{Disc}\propto R^2$

Therefore,

$\frac{I_1}{I_2}=\frac{R_1^2}{R_2^2}$

$\frac{I_1}{I_2}=\frac{{\left(.2\right)}^2}{{\left({.6}^{}\right)}^2}$ $=\frac{1}{9}$.